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1
Yamaga, Kazuki. « Stochastic Process Emerged from Lattice Fermion Systems by Repeated Measurements and Long-Time Limit ». Axioms 9, no 3 (29 juillet 2020) : 90. http://dx.doi.org/10.3390/axioms9030090.
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It is known that, in quantum theory, measurements may suppress Hamiltonian dynamics of a system. A famous example is the ‘Quantum Zeno Effect’. This is the phenomena that, if one performs the measurements M times asking whether the system is in the same state as the one at the initial time until the fixed measurement time t, then survival probability tends to 1 by taking the limit M→∞. This is the case for fixed measurement time t. It is known that, if one takes measurement time infinite at appropriate scaling, the ‘Quantum Zeno Effect’ does not occur and the effect of Hamiltonian dynamics emerges. In the present paper, we consider the long time repeated measurements and the dynamics of quantum many body systems in the scaling where the effect of measurements and dynamics are balanced. We show that the stochastic process, called the symmetric simple exclusion process (SSEP), is obtained from the repeated and long time measurements of configuration of particles in finite lattice fermion systems. The emerging stochastic process is independent of potential and interaction of the underlying Hamiltonian of the system.
2
Brandner, Kay. « Coherent Transport in Periodically Driven Mesoscopic Conductors : From Scattering Amplitudes to Quantum Thermodynamics ». Zeitschrift für Naturforschung A 75, no 5 (26 mai 2020) : 483–500. http://dx.doi.org/10.1515/zna-2020-0056.
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AbstractScattering theory is a standard tool for the description of transport phenomena in mesoscopic systems. Here, we provide a detailed derivation of this method for nano-scale conductors that are driven by oscillating electric or magnetic fields. Our approach is based on an extension of the conventional Lippmann–Schwinger formalism to systems with a periodically time-dependent Hamiltonian. As a key result, we obtain a systematic perturbation scheme for the Floquet scattering amplitudes that describes the transition of a transport carrier through a periodically driven sample. Within a general multi-terminal setup, we derive microscopic expressions for the mean values and time-integrated correlation functions, or zero-frequency noise, of matter and energy currents, thus recovering the results of earlier studies in a unifying framework. We show that this framework is inherently consistent with the first and the second law of thermodynamics and prove that the mean rate of entropy production vanishes only if all currents in the system are zero. As an application, we derive a generalized Green–Kubo relation, which makes it possible to express the response of any mean currents to small variations of temperature and chemical potential gradients in terms of time integrated correlation functions between properly chosen currents. Finally, we discuss potential topics for future studies and further reaching applications of the Floquet scattering approach to quantum transport in stochastic and quantum thermodynamics.
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Müller, Matthias M., Stefano Gherardini, Nicola Dalla Pozza et Filippo Caruso. « Noise sensing via stochastic quantum Zeno ». Physics Letters A 384, no 13 (mai 2020) : 126244. http://dx.doi.org/10.1016/j.physleta.2020.126244.
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Müller, Matthias M., Stefano Gherardini et Filippo Caruso. « Quantum Zeno Dynamics Through Stochastic Protocols ». Annalen der Physik 529, no 9 (21 juillet 2017) : 1600206. http://dx.doi.org/10.1002/andp.201600206.
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Facchi, P., et S. Pascazio. « Quantum Zeno Phenomena : Pulsed versus Continuous Measurement ». Fortschritte der Physik 49, no 10-11 (octobre 2001) : 941. http://dx.doi.org/10.1002/1521-3978(200110)49:10/11<941 ::aid-prop941>3.0.co;2-v.
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Gherardini, Stefano, Shamik Gupta, Francesco Saverio Cataliotti, Augusto Smerzi, Filippo Caruso et Stefano Ruffo. « Stochastic quantum Zeno by large deviation theory ». New Journal of Physics 18, no 1 (25 janvier 2016) : 013048. http://dx.doi.org/10.1088/1367-2630/18/1/013048.
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Power, W. L., et P. L. Knight. « Stochastic simulations of the quantum Zeno effect ». Physical Review A 53, no 2 (1 février 1996) : 1052–59. http://dx.doi.org/10.1103/physreva.53.1052.
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Chaudhari, Abhijit P., Shane P. Kelly, Riccardo J. Valencia-Tortora et Jamir Marino. « Zeno crossovers in the entanglement speed of spin chains with noisy impurities ». Journal of Statistical Mechanics : Theory and Experiment 2022, no 10 (1 octobre 2022) : 103101. http://dx.doi.org/10.1088/1742-5468/ac8e5d.
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Abstract We use a noisy signal with finite correlation time to drive a spin (dissipative impurity) in the quantum XY spin chain and calculate the dynamics of entanglement entropy (EE) of a bipartition of spins, for a stochastic quantum trajectory. We compute the noise averaged EE of a bipartition of spins and observe that its speed of spreading decreases at strong dissipation, as a result of the Zeno effect. We recover the Zeno crossover and show that noise averaged EE can be used as a proxy for the heating and Zeno regimes. Upon increasing the correlation time of the noise, the location of the Zeno crossover shifts at stronger dissipation, extending the heating regime.
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Biella, Alberto, et Marco Schiró. « Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition ». Quantum 5 (19 août 2021) : 528. http://dx.doi.org/10.22331/q-2021-08-19-528.
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It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.
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Shushin, A. I. « The effect of measurements, randomly distributed in time, on quantum systems : stochastic quantum Zeno effect ». Journal of Physics A : Mathematical and Theoretical 44, no 5 (4 janvier 2011) : 055303. http://dx.doi.org/10.1088/1751-8113/44/5/055303.
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Kurizki, Gershon. « Universal Dynamical Control of Open Quantum Systems ». ISRN Optics 2013 (19 septembre 2013) : 1–51. http://dx.doi.org/10.1155/2013/783865.
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Due to increasing demands on speed and security of data processing, along with requirements on measurement precision in fundamental research, quantum phenomena are expected to play an increasing role in future technologies. Special attention must hence be paid to omnipresent decoherence effects, which hamper quantumness. Their consequence is always a deviation of the quantum state evolution (error) with respect to the expected unitary evolution if these effects are absent. In operational tasks such as the preparation, transformation, transmission, and detection of quantum states, these effects are detrimental and must be suppressed by strategies known as dynamical decoupling, or the more general dynamical control by modulation developed by us. The underlying dynamics must be Zeno-like, yielding suppressed coupling to the bath. There are, however, tasks which cannot be implemented by unitary evolution, in particular those involving a change of the system’s state entropy. Such tasks necessitate efficient coupling to a bath for their implementation. Examples include the use of measurements to cool (purify) a system, to equilibrate it, or to harvest and convert energy from the environment. If the underlying dynamics is anti-Zeno like, enhancement of this coupling to the bath will occur and thereby facilitate the task, as discovered by us. A general task may also require state and energy transfer, or entanglement of noninteracting parties via shared modes of the bath which call for maximizing the shared (two-partite) couplings with the bath, but suppressing the single-partite couplings. For such tasks, a more subtle interplay of Zeno and anti-Zeno dynamics may be optimal. We have therefore constructed a general framework for optimizing the way a system interacts with its environment to achieve a desired task. This optimization consists in adjusting a given “score” that quantifies the success of the task, such as the targeted fidelity, purity, entropy, entanglement, or energy by dynamical modification of the system-bath coupling spectrum on demand.
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LAN, LI-LI, XIANG-BIN WANG et SHAO-MING FEI. « PHOTON INDUCED ENTANGLEMENT IN ATOM-CAVITY SYSTEMS ». International Journal of Quantum Information 08, no 08 (décembre 2010) : 1239–50. http://dx.doi.org/10.1142/s0219749910006976.
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We study the evolution of quantum entanglement in double cavity systems. The entanglement of cavity atoms induced by entangled pair of photons is investigated. Both entanglement sudden death and entanglement sudden birth phenomena are shown to exist and are analyzed in detail. We also propose a strategy to enhance the entanglement between the atom in one cavity and the photon in another cavity by using quantum Zeno effect.
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HÜFFEL, HELMUTH. « NONLINEAR PHENOMENA IN CANONICAL STOCHASTIC QUANTIZATION ». International Journal of Bifurcation and Chaos 18, no 09 (septembre 2008) : 2787–91. http://dx.doi.org/10.1142/s0218127408022019.
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Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochastic process. We discuss a novel formulation of the Higgs mechanism in QED.
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Gherardini, Stefano, Andrea Smirne, Matthias M. Müller et Filippo Caruso. « Advances in Sequential Measurement and Control of Open Quantum Systems ». Proceedings 12, no 1 (24 juin 2019) : 11. http://dx.doi.org/10.3390/proceedings2019012011.
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Novel concepts, perspectives and challenges in measuring and controlling an open quantum system via sequential schemes are shown. We discuss how similar protocols, relying both on repeated quantum measurements and dynamical decoupling control pulses, can allow to: (i) Confine and protect quantum dynamics from decoherence in accordance with the Zeno physics. (ii) Analytically predict the probability that a quantum system is transferred into a target quantum state by means of stochastic sequential measurements. (iii) Optimally reconstruct the spectral density of environmental noise sources by orthogonalizing in the frequency domain the filter functions driving the designed quantum-sensor. The achievement of these tasks will enhance our capability to observe and manipulate open quantum systems, thus bringing advances to quantum science and technologies.
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BHATTACHARYA, B., et K. HAJRA. « QUANTUM FIELD THEORY OF A DISSIPATIVE SYSTEM ». Modern Physics Letters A 10, no 06 (28 février 1995) : 467–77. http://dx.doi.org/10.1142/s0217732395000508.
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Quantum dissipative scalar and fermionic fields are studied here from classical stochastic fields. These classical stochastic fields are the outcome of the relativistic generalization of Nelson's stochastic mechanics based on a new microlocal geometry. Results show that the dissipation is the external classical phenomena whereas quantum nature comes from within (microlocal structure).
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Castro Santis, Ricardo. « Quantum stochastic dynamics in multi-photon optics ». Infinite Dimensional Analysis, Quantum Probability and Related Topics 17, no 01 (mars 2014) : 1450007. http://dx.doi.org/10.1142/s0219025714500076.
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Multi-photon models are theoretically and experimentally important because in them quantum properly phenomena are verified; as well as squeezed light and quantum entanglement also play a relevant role in quantum information and quantum communication (see Refs. 18–20).In this paper we study a generic model of a multi-photon system with an arbitrary number of pumping and subharmonics fields. This model includes measurement on the system, as could be direct or homodyne detection and we demonstrate the existence of dynamics in the context of Continuous Measurement Theory of Open Quantum Systems (see Refs. 1–11) using Quantum Stochastic Differential Equations with unbounded coefficients (see Refs. 10–15).
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Albeverio, Sergio, et Sonia Mazzucchi. « Infinite dimensional integrals and partial differential equations for stochastic and quantum phenomena ». Journal of Geometric Mechanics 11, no 2 (2019) : 123–37. http://dx.doi.org/10.3934/jgm.2019006.
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Beyer, Michael, et Wolfgang Paul. « On the Stochastic Mechanics Foundation of Quantum Mechanics ». Universe 7, no 6 (27 mai 2021) : 166. http://dx.doi.org/10.3390/universe7060166.
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Among the famous formulations of quantum mechanics, the stochastic picture developed since the middle of the last century remains one of the less known ones. It is possible to describe quantum mechanical systems with kinetic equations of motion in configuration space based on conservative diffusion processes. This leads to the representation of physical observables through stochastic processes instead of self-adjoint operators. The mathematical foundations of this approach were laid by Edward Nelson in 1966. It allows a different perspective on quantum phenomena without necessarily using the wave-function. This article recaps the development of stochastic mechanics with a focus on variational and extremal principles. Furthermore, based on recent developments of optimal control theory, the derivation of generalized canonical equations of motion for quantum systems within the stochastic picture are discussed. These so-called quantum Hamilton equations add another layer to the different formalisms from classical mechanics that find their counterpart in quantum mechanics.
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Aris Chatzidimitriou-Dreismann, C. « Quantumness of correlations in nanomaterials—experimental evidence and unconventional effects ». AIMS Materials Science 9, no 3 (2022) : 382–405. http://dx.doi.org/10.3934/matersci.2022023.
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<abstract><p>Quantum correlations phenomena, such as entanglement, quantum discord and quantum coherence, are ubiquitous effects caused by interactions between physical systems—such as electrons and ions in a piece of metal, or H atoms/molecules adsorbed in nanoporous materials. Here, we address time-asymmetric quantumness of correlations (QoC), with particular emphasis on their energetic consequences for dynamics and non-equilibrium thermodynamics in condensed matter and/or many-body systems. Some known theoretical models—for example, the quantum Zeno effect and GKSL-type Markovian equations-of-motion, all of them being time-asymmetric—are shortly considered, with emphasis on the general character of one of their common and most intriguing result. Namely, that in clear contradistinction to conventional expectations, degradation (or destruction, decoherence, consumption, smearing out, coarse-graining) of quantum correlations can be a source of work (instead of heat production). The experimental relevance of the theoretical considerations is shown with the aid of a recent scattering experiment exploring the impulsively driven (by neutron collisions) translational dynamics of H$ _2 $ molecules in carbon nanotubes and other nanostructured materials—a topic of immediate relevance for material sciences and related technologies.</p></abstract>
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Mohammed, Wael W., Farah M. Al-Askar, Clemente Cesarano et M. El-Morshedy. « Solitary Wave Solutions of the Fractional-Stochastic Quantum Zakharov–Kuznetsov Equation Arises in Quantum Magneto Plasma ». Mathematics 11, no 2 (16 janvier 2023) : 488. http://dx.doi.org/10.3390/math11020488.
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In this paper, we consider the (3 + 1)-dimensional fractional-stochastic quantum Zakharov–Kuznetsov equation (FSQZKE) with M-truncated derivative. To find novel trigonometric, hyperbolic, elliptic, and rational fractional solutions, two techniques are used: the Jacobi elliptic function approach and the modified F-expansion method. We also expand on a few earlier findings. The extended quantum Zakharov–Kuznetsov has practical applications in dealing with quantum electronpositron–ion magnetoplasmas, warm ions, and hot isothermal electrons in the presence of uniform magnetic fields, which makes the solutions obtained useful in analyzing a number of intriguing physical phenomena. We plot our data in MATLAB and display various 3D and 2D graphical representations to explain how the stochastic term and fractional derivative influence the exact solutions of the FSEQZKE.
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Cremaschini, Claudio, et Massimo Tessarotto. « Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity ». Entropy 23, no 5 (23 avril 2021) : 511. http://dx.doi.org/10.3390/e23050511.
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A new type of quantum correction to the structure of classical black holes is investigated. This concerns the physics of event horizons induced by the occurrence of stochastic quantum gravitational fields. The theoretical framework is provided by the theory of manifestly covariant quantum gravity and the related prediction of an exclusively quantum-produced stochastic cosmological constant. The specific example case of the Schwarzschild–deSitter geometry is looked at, analyzing the consequent stochastic modifications of the Einstein field equations. It is proved that, in such a setting, the black hole event horizon no longer identifies a classical (i.e., deterministic) two-dimensional surface. On the contrary, it acquires a quantum stochastic character, giving rise to a frame-dependent transition region of radial width δr between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass M of the black hole, scaling as δr∼M3; (b) for supermassive black holes δr is typically orders of magnitude larger than the Planck length lP. Instead, for typical stellar-mass black holes, δr may drop well below lP. The outcome provides new insight into the quantum properties of black holes, with implications for the physics of quantum tunneling phenomena expected to arise across stochastic event horizons.
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Martín-Pasquín, Francisco Javier, et Alexander N. Pisarchik. « Brownian Behavior in Coupled Chaotic Oscillators ». Mathematics 9, no 19 (6 octobre 2021) : 2503. http://dx.doi.org/10.3390/math9192503.
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Since the dynamical behavior of chaotic and stochastic systems is very similar, it is sometimes difficult to determine the nature of the movement. One of the best-studied stochastic processes is Brownian motion, a random walk that accurately describes many phenomena that occur in nature, including quantum mechanics. In this paper, we propose an approach that allows us to analyze chaotic dynamics using the Langevin equation describing dynamics of the phase difference between identical coupled chaotic oscillators. The time evolution of this phase difference can be explained by the biased Brownian motion, which is accepted in quantum mechanics for modeling thermal phenomena. Using a deterministic model based on chaotic Rössler oscillators, we are able to reproduce a similar time evolution for the phase difference. We show how the phenomenon of intermittent phase synchronization can be explained in terms of both stochastic and deterministic models. In addition, the existence of phase multistability in the phase synchronization regime is demonstrated.
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French, O. E., K. I. Hopcraft, E. Jakeman et T. J. Shepherd. « Intrinsic and measured statistics of discrete stochastic populations ». Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences 464, no 2099 (17 juin 2008) : 2929–48. http://dx.doi.org/10.1098/rspa.2008.0110.
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The notion that the nature of a measurement is critical to its outcome is usually associated with quantum phenomena. In this paper, we show that the observed statistical properties are also a function of the measurement technique in the case of simple classical populations. In particular, the measured and intrinsic statistics of a single population may be different, while correlation and transfer of individuals between two populations may be hidden from the observer.
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Hnatič, Michal, Juha Honkonen et Tomáš Lučivjanský. « Symmetry Breaking in Stochastic Dynamics and Turbulence ». Symmetry 11, no 10 (23 septembre 2019) : 1193. http://dx.doi.org/10.3390/sym11101193.
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Symmetries play paramount roles in dynamics of physical systems. All theories of quantum physics and microworld including the fundamental Standard Model are constructed on the basis of symmetry principles. In classical physics, the importance and weight of these principles are the same as in quantum physics: dynamics of complex nonlinear statistical systems is straightforwardly dictated by their symmetry or its breaking, as we demonstrate on the example of developed (magneto)hydrodynamic turbulence and the related theoretical models. To simplify the problem, unbounded models are commonly used. However, turbulence is a mesoscopic phenomenon and the size of the system must be taken into account. It turns out that influence of outer length of turbulence is significant and can lead to intermittency. More precisely, we analyze the connection of phenomena such as behavior of statistical correlations of observable quantities, anomalous scaling, and generation of magnetic field by hydrodynamic fluctuations with symmetries such as Galilean symmetry, isotropy, spatial parity and their violation and finite size of the system.
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Rauch, H. « Mysterious Quantum Effects Observed with Neutrons ». Ukrainian Journal of Physics 57, no 4 (30 avril 2012) : 469. http://dx.doi.org/10.15407/ujpe57.4.469.
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Single-particle interference phenomena can be observed with neutrons, and the "entanglement of degrees of freedom", i.e. the contextuality, can be verified and used in further experiments. Entanglement of two photons or atoms is a complementary situation to the double-slit diffraction of a single photon, neutron, or atom. In this respect, neutrons are proper tools for testing quantum mechanics, because they are massive, they couple to electromagnetic fields due to their magnetic moment, and they are subject to all basic interactions, and they are sensitive to topological effects as well. The4π-symmetry of spinor wave functions, the spin-superposition law, and many topological phenomena can be made visible, which shows interesting intrinsic features of quantum physics. Related experiments will be discussed. Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Recent neutron interferometry experiments based on post-selection methods have renewed the discussion about quantum non-locality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in the phase space even in cases of spatially separated Schrödinger cat-like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other de-coherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle.
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ORTIZ, G., et M. D. JONES. « EXPLORING THE QUANTUM WORLD OF COMPLEX STATES ». International Journal of Modern Physics B 13, no 05n06 (10 mars 1999) : 525–34. http://dx.doi.org/10.1142/s0217979299000424.
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Solving the fundamental microscopic equations of interacting quantum particles is a goal of many-body physicists. Statistical methods reduce the complexity of the problem by sampling phase space selectively using random-walks and real states. Many interesting physical phenomena (e.g., electrons in external magnetic fields) involve systems whose state functions are inherently complex-valued. The Fixed-Phase method is a stochastic approach to deal with such problems. Its key ingredient is a trial phase that plays the role of gauge function in the transformation that maps the original fermion (or boson) problem to a boson problem for the modulus of the state function. The Released-Phase method relaxes that constraint and allows us to obtain, in principle, the "exact" properties, although it is subjected to the infamous "phase problem." In our tour of the (complex) Quantum World, we will show how these methods have been successfully applied to a wide variety of physical phenomena ranging from quantum Hall topological fluids and Wigner crystals to the study of the core structure of vortices in superfluid 4 He and atomic systems in superstrong magnetic fields found in astrophysical settings.
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GHIKAS, DEMETRIS P. K., et ATHANASIOS C. TZEMOS. « STOCHASTIC ANTI-RESONANCE IN THE TIME EVOLUTION OF INTERACTING QUBITS ». International Journal of Quantum Information 10, no 02 (mars 2012) : 1250023. http://dx.doi.org/10.1142/s0219749912500232.
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We investigate the possibility of appearance of new phenomena derived from the influence of noise on quantum systems. As a starting point we study the entanglement evolution of two coupled qubits in interaction with an external environment and in the presence of an external magnetic field with a stochastic component. The results show the expected degradation of entanglement due to the noise. The new effect is that for particular initial states the time of disentanglement depends in a non-monotonous way on the strength of the noise. We find that it is shortest for an intermediate strength value of the noise. This we call "stochastic anti-resonance." Our new result indicates that there are noise values which are particularly harmful and should be avoided. This could lead to a better understanding of noisy perturbations and their role for optimal designing of quantum devices.
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NAMSRAI, KH, YA HULREE et N. NJAMTSEREN. « AN OVERVIEW OF THE APPLICATION OF THE LANGEVIN EQUATION TO THE DESCRIPTION OF BROWNIAN AND QUANTUM MOTIONS OF A PARTICLE ». International Journal of Modern Physics A 07, no 12 (10 mai 1992) : 2661–77. http://dx.doi.org/10.1142/s0217751x92001198.
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A simple scheme of unified description of different physical phenomena by using the Langevin type equations is reviewed. Within this approach much attention is being paid to the study of Brownian and quantum motions. Stochastic equations with a white noise term give all characteristics of the Brownian motion. Some generalization of the Langevin type equations allows us to obtain nonlinear equations of particles' motion, which are formally equivalent to the Schrödinger equation. Thus, we establish Nelson's stochastic mechanics on the basis of the Langevin equation.
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Kim, Eun-jin. « Investigating Information Geometry in Classical and Quantum Systems through Information Length ». Entropy 20, no 8 (3 août 2018) : 574. http://dx.doi.org/10.3390/e20080574.
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Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate underlying principles governing different phenomena, it is extremely valuable to utilise a mathematical tool that is not specific to a particular system. We provide such a tool based on information geometry by quantifying the similarity and disparity between Probability Density Functions (PDFs) by a metric such that the distance between two PDFs increases with the disparity between them. Specifically, we invoke the information length L(t) to quantify information change associated with a time-dependent PDF that depends on time. L(t) is uniquely defined as a function of time for a given initial condition. We demonstrate the utility of L(t) in understanding information change and attractor structure in classical and quantum systems.
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Badibi, O. C., I. Ramadhani, M. A. Ndondo et S. D. Kumwimba. « Numerical Stabilities of Vasicek and Geometric Brownian Motion Models ». European Journal of Mathematical Analysis 3 (9 janvier 2023) : 8. http://dx.doi.org/10.28924/ada/ma.3.8.
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Stochastic differential equations (SDEs) are very often used as models for a large number of phenomena in the physical, economic and management sciences. They generalize the notion of ordinary differential equations, taking into account a white additive and multiplicative noise term, to model random trajectories such as stock market prices or particles movements, on the quantum scale, subject to diffusion phenomena. In rare cases, it is generally impossible to have explicit solution to these equations. In this case, the numerical approach, presenting itself under various aspects, is the only favorable outcome. However, the stability of numerical schemes for stochastic differential equations solution is much more significant. In this paper, we establish and make a classical proof of the mean and mean-square stabilities of the numerical SDEs schemes for Vasicek and Geometric Brownian motion models.
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Ye, Xiaoqian, Sumei Huang, Li Deng et Aixi Chen. « Improving the Stochastic Feedback Cooling of a Mechanical Oscillator Using a Degenerate Parametric Amplifier ». Photonics 9, no 4 (16 avril 2022) : 264. http://dx.doi.org/10.3390/photonics9040264.
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Cooling of a macroscopic mechanical resonator to extremely low temperatures is a necessary condition to observe a variety of macroscopic quantum phenomena. Here, we study the stochastic feedback cooling of a mechanical resonator in an optomechanical system with a degenerate optical parametric amplifier (OPA). In the bad-cavity limit, we find that the OPA can enhance the cooling of the movable mirror in the stochastic feedback cooling scheme. The movable mirror can be cooled from 132 mK to 0.033 mK, which is lower than that without the OPA by a factor of about 5.
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Zhang, Li, et Xiu Hua Yuan. « Stochastic Resonance in a Single-Mode Laser System with an Input Pulse Signal ». Key Engineering Materials 552 (mai 2013) : 377–83. http://dx.doi.org/10.4028/www.scientific.net/kem.552.377.
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In this paper, we investigated the stochastic resonance (SR) phenomenon in a laser system with correlated pump noise and quantum noise. The signal-to-noise ratio (SNR) is calculated when a square sine pulse signal is added to the system. The effects of the duty cycle of pulse signal and the correlation strength of noises on the SNR are discussed. Some valuable phenomena are investigated to improve the output SNR of laser.
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Boixo, S., E. Knill et R. Somma. « Eigenpath traversal by phase randomization ». Quantum Information and Computation 9, no 9&10 (septembre 2009) : 833–55. http://dx.doi.org/10.26421/qic9.9-10-7.
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A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply the instantaneous Hamiltonian for a random time. The resulting decoherence approximates a projective measurement onto the desired eigenstate, achieving a version of the quantum Zeno effect. If negative evolution times can be implemented with constant overhead, then the average absolute evolution time required by our method is $\cO(L^{2} /\Delta)$ for constant error probability, where $L$ is the length of the path of eigenstates and $\Delta$ is the minimum spectral gap of the Hamiltonian. The dependence of the cost on $\Delta$ is optimal. Making explicit the dependence on the path length is useful for cases where $L$ is much less than the general bound. The complexity of our method has a logarithmic improvement over previous algorithms of this type. The same cost applies to the discrete-time case, where a family of unitary operators is given and each unitary and its inverse can be used. Restriction to positive evolution times incurs an error that decreases exponentially with the cost. Applications of this method to unstructured search and quantum sampling are considered. In particular, we discuss the quantum simulated annealing algorithm for solving combinatorial optimization problems. This algorithm provides a quadratic speed-up in the gap of the stochastic matrix over its classical counterpart implemented via Markov chain Monte Carlo.
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Pekola, J. P., et I. M. Khaymovich. « Thermodynamics in Single-Electron Circuits and Superconducting Qubits ». Annual Review of Condensed Matter Physics 10, no 1 (10 mars 2019) : 193–212. http://dx.doi.org/10.1146/annurev-conmatphys-033117-054120.
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Classical and quantum electronic circuits provide ideal platforms to investigate stochastic thermodynamics, and they have served as a stepping stone to realize Maxwell's Demons with highly controllable protocols. In this article, we first review the central thermal phenomena in quantum nanostructures. Thermometry and basic refrigeration methods are described as enabling tools for thermodynamics experiments. Next, we discuss the role of information in thermodynamics that leads to the concept of Maxwell's Demon. Various Maxwell's Demons realized in single-electron circuits over the past couple of years are described. Currently, true quantum thermodynamics in superconducting circuits is a focus of attention, and we end the review by discussing the ideas and first experiments in this exciting area of research.
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Gebhart, Valentin, Kyrylo Snizhko, Thomas Wellens, Andreas Buchleitner, Alessandro Romito et Yuval Gefen. « Topological transition in measurement-induced geometric phases ». Proceedings of the National Academy of Sciences 117, no 11 (2 mars 2020) : 5706–13. http://dx.doi.org/10.1073/pnas.1911620117.
Texte intégralRésumé :
The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous and also underline the physics of robust topological phenomena such as the quantum Hall effect. Equivalently, a geometric phase may be induced through a cyclic sequence of quantum measurements. We show that the application of a sequence of weak measurements renders the closed trajectories, hence the geometric phase, stochastic. We study the concomitant probability distribution and show that, when varying the measurement strength, the mapping between the measurement sequence and the geometric phase undergoes a topological transition. Our finding may impact measurement-induced control and manipulation of quantum states—a promising approach to quantum information processing. It also has repercussions on understanding the foundations of quantum measurement.
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ZENG, CHUNHUA, AILING GONG et YUHUI LUO. « EFFECT OF ASYMMETRY IN A BISTABLE SYSTEM WITH QUANTUM FLUCTUATIONS : STRONG FRICTION LIMIT ». International Journal of Modern Physics B 25, no 32 (30 décembre 2011) : 4331–38. http://dx.doi.org/10.1142/s0217979211059255.
Texte intégralRésumé :
In this paper, we study the effect of asymmetry of the potential in a bistable system with quantum fluctuations. Within the quantum Smoluchowski regime, the expressions for the mean first passage time (MFPT) and signal-to-noise ratio (SNR) of the system are obtained, respectively. Based on the MFPT and SNR, we consider both, the overdamped quantum case and its classical counterpart, the effects of the quantum fluctuations and the asymmetry of the potential on the MFPT and SNR are discussed. Our main results show that (i) the quantum fluctuations facilitate the particle to reach the destination from its original position, (ii) the resonant activation (RA) phenomena can be observed with varying asymmetry of the potential, and (iii) the quantum effects in an asymmetric bistable system about SNR are prominent for lower temperatures and smaller asymmetry of the potential. Moreover, the quantum effects enhance the stochastic resonance (SR) of the system.
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ACCARDI, LUIGI. « NOISE AND DISSIPATION IN QUANTUM THEORY ». Reviews in Mathematical Physics 02, no 02 (janvier 1990) : 127–76. http://dx.doi.org/10.1142/s0129055x90000065.
Texte intégralRésumé :
A model independent generalization of quantum mechanics, including the usual as well as the dissipative quantum systems, is proposed. The theory is developed deductively from the basic principles of the standard quantum theory, the only new qualitative assumption being that we allow the wave operator at time t of a quantum system to be non-differentiable (in t) in the usual sense, but only in an appropriately defined (Sec. 5) stochastic sense. The resulting theory is shown to lead to a natural generalization of the usual quantum equations of motion, both in the form of the Schrödinger equation in interaction representation (Sec. 6) and of the Heisenberg equation (Sec. 8). The former equation leads in particular to a quantum fluctuation-dissipation relation of Einstein’s type. The latter equation is a generalized Langevin equation, from which the known form of the generalized master equation can be deduced via the quantum Feynmann-Kac technique (Secs. 9 and 10). For quantum noises with increments commuting with the past the quantum Langevin equation defines a closed system of (usually nonlinear) stochastic differential equations for the observables defining the coefficients of the noises. Such systems are parametrized by certain Lie algebras of observables of the system (Sec. 10). With appropriate choices of these Lie algebras one can deduce generalizations and corrections of several phenomenological equations previously introduced at different times to explain different phenomena. Two examples are considered: the Lie algebra [q, p]=i (Sec. 12), which is shown to lead to the equations of the damped harmonic oscillator; and the Lie algebra of SO(3) (Sec. 13) which is shown to lead to the Bloch equations. In both cases the equations obtained are independent of the model of noise. Moreover, in the former case, it is proved that the only possible noises which preserve the commutation relations of p, q are the quantum Brownian motions, commonly used in laser theory and solid state physics.
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Mouslih, S., M. Jakha, I. Dahiri, S. Taj, B. Manaut et E. Siher. « New phenomena in laser-assisted leptonic decays of the negatively charged boson W − ». Physica Scripta 97, no 4 (24 mars 2022) : 045306. http://dx.doi.org/10.1088/1402-4896/ac5d6e.
Texte intégralRésumé :
Abstract The majority of studies and experiments performed at electron-positron colliders over the last two decades have focused on studying W and Z weak force-carrying bosons and accurately measuring all their properties, not only because they play an important role in establishing Standard Model theory and providing an accurate test of its predictions of particle interactions, but also because they are a unique tool for probing manifestations of the new physics beyond the standard model. Therefore, it would be particularly important to discuss some of the new phenomena and changes that can arise in these bosons when their decay occurs under an external electromagnetic field. In a recent paper, we investigated the laser effect on the final products of Z boson decay and found that laser had an unprecedented effect on branching ratios. In this work and within the standard Glashow-Weinberg-Salam model of electroweak interactions, we study theoretically the leptonic decay of the W −-boson ( W − → ℓ − ν ¯ ℓ ) in the presence of a circularly polarized electromagnetic field and we examine the laser effect, in terms of its field strength and frequency, on the leptonic decay rate and the phenomenon of multiphoton processes. The calculations are carried out using the exact relativistic wave functions of charged particles in an electromagnetic field. It was found that the laser significantly contributed to reducing the probability of W −-boson decay. We show that the laser-assisted decay rate is equal to the laser-free one only when the famous Kroll-Watson sum rule is fulfilled. The notable effect of the laser on the leptonic decay rate was reasonably interpreted by the well-known quantum Zeno effect or by the opening of channels other than leptonic ones to decay. This work will pave the way for an upcoming one to study the hadronic decay of the W −-boson and then explore the laser effect on its lifetime and branching ratios.
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Frank, T. D. « Strongly Nonlinear Stochastic Processes in Physics and the Life Sciences ». ISRN Mathematical Physics 2013 (28 mars 2013) : 1–28. http://dx.doi.org/10.1155/2013/149169.
Texte intégralRésumé :
Strongly nonlinear stochastic processes can be found in many applications in physics and the life sciences. In particular, in physics, strongly nonlinear stochastic processes play an important role in understanding nonlinear Markov diffusion processes and have frequently been used to describe order-disorder phase transitions of equilibrium and nonequilibrium systems. However, diffusion processes represent only one class of strongly nonlinear stochastic processes out of four fundamental classes of time-discrete and time-continuous processes evolving on discrete and continuous state spaces. Moreover, strongly nonlinear stochastic processes appear both as Markov and non-Markovian processes. In this paper the full spectrum of strongly nonlinear stochastic processes is presented. Not only are processes presented that are defined by nonlinear diffusion and nonlinear Fokker-Planck equations but also processes are discussed that are defined by nonlinear Markov chains, nonlinear master equations, and strongly nonlinear stochastic iterative maps. Markovian as well as non-Markovian processes are considered. Applications range from classical fields of physics such as astrophysics, accelerator physics, order-disorder phase transitions of liquids, material physics of porous media, quantum mechanical descriptions, and synchronization phenomena in equilibrium and nonequilibrium systems to problems in mathematics, engineering sciences, biology, psychology, social sciences, finance, and economics.
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Wu, Yusen, et Jingbo B. Wang. « Estimating Gibbs partition function with quantum Clifford sampling ». Quantum Science and Technology 7, no 2 (14 février 2022) : 025006. http://dx.doi.org/10.1088/2058-9565/ac47f0.
Texte intégralRésumé :
Abstract The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum systems and phenomena. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantum–classical algorithm to estimate the partition function, utilising a novel quantum Clifford sampling technique. Note that previous works on the estimation of partition functions require O ( 1 / ϵ Δ ) -depth quantum circuits (Srinivasan et al 2021 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) pp 112–22; Montanaro 2015 Proc. R. Soc. A 471 20150301), where Δ is the minimum spectral gap of stochastic matrices and ϵ is the multiplicative error. Our algorithm requires only a shallow O ( 1 ) -depth quantum circuit, repeated O ( n / ϵ 2 ) times, to provide a comparable ϵ approximation. Shallow-depth quantum circuits are considered vitally important for currently available noisy intermediate-scale quantum devices.
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Cilluffo, Dario. « Statistical time-domain characterization of non-periodic optical clocks ». Quantum 6 (14 juillet 2022) : 764. http://dx.doi.org/10.22331/q-2022-07-14-764.
Texte intégralRésumé :
Measuring time means counting the occurrence of periodic phenomena. Over the past centuries a major effort was put to make stable and precise oscillators to be used as clock regulators. Here we consider a different class of clocks based on stochastic clicking processes. We provide a rigorous statistical framework to study the performances of such devices and apply our results to a single coherently driven two-level atom under photodetection as an extreme example of non-periodic clock. Quantum Jump MonteCarlo simulations and photon counting waiting time distribution will provide independent checks on the main results.
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Muscato, Orazio. « A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation ». Communications in Applied and Industrial Mathematics 8, no 1 (20 décembre 2017) : 237–50. http://dx.doi.org/10.1515/caim-2017-0012.
Texte intégralRésumé :
Abstract The Wigner equation represents a promising model for the simulation of electronic nanodevices, which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. During these years, a Monte Carlo technique for the solution of this kinetic equation has been developed, based on the generation and annihilation of signed particles. This technique can be deeply understood in terms of the theory of pure jump processes with a general state space, producing a class of stochastic algorithms. One of these algorithms has been validated successfully by numerical experiments on a benchmark test case.
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XU, DE-SHENG, LI CAO et DA-JIN WU. « STOCHASTIC RESONANCE IN A SINGLE-MODE LASER DRIVEN BY QUADRATIC COLORED PUMP NOISE AND QUANTUM NOISE WITH CROSS-CORRELATION BETWEEN REAL AND IMAGINARY PARTS OF NOISE ». International Journal of Modern Physics B 23, no 22 (10 septembre 2009) : 4665–74. http://dx.doi.org/10.1142/s021797920905300x.
Texte intégralRésumé :
Based on the single-mode laser noise model driven by quadratic colored pump noise and quantum noise with cross-correlation between real and imaginary parts of noise proposed in International Journal of Modern Physics B20, 5383 (2006) and Phys. Rev. E 73, 023802 (2006), the stochastic resonance (SR) of laser intensity is investigated by virtue of the linearized approximation. The analytic expression of signal-to-noise ratio (SNR) is calculated. It is found that the phenomena of stochastic resonance respectively exist in the curves of the SNR versus the noise cross-correlation coefficient λp and the SNR versus the pump parameter a, as well as the SNR versus the signal frequency [Formula: see text] for the model. It is shown that there are three different types of SR in the model: the conventional form of SR, the SR in the broad sense and the bona fide SR.
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Das, Debraj, Sushanta Dattagupta et Shamik Gupta. « Quantum unitary evolution interspersed with repeated non-unitary interactions at random times : the method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain ». Journal of Statistical Mechanics : Theory and Experiment 2022, no 5 (1 mai 2022) : 053101. http://dx.doi.org/10.1088/1742-5468/ac6256.
Texte intégralRésumé :
Abstract In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical framework to obtain the average density operator of the system at any time during the dynamical evolution. The average is with respect to the classical randomness associated with the random time intervals between successive interactions, which we consider to be independent and identically-distributed random variables. The formalism is very general in that it applies to any quantum system, to any form of non-unitary interaction, and to any probability distribution for the random times. We provide two explicit applications of the formalism in the context of the so-called tight-binding model relevant in various contexts in solid-state physics, e.g. in modelling nano wires. Considering the case of one dimension, the corresponding tight-binding chain models the motion of a charged particle between the sites of a lattice, wherein the particle is for most times localized on the sites, owing to spontaneous quantum fluctuations tunnels between the nearest-neighbour sites. We consider two representative forms of interactions, one that implements a stochastic reset of quantum dynamics in which the density operator is at random times reset to its initial form, and one in which projective measurements are performed on the system at random times. In the former case, we demonstrate with our exact results how the particle is localized on the sites at long times, leading to a time-independent mean-squared displacement (MSD) of the particle about its initial location. This stands in stark contrast to the behavior in the absence of interactions, when the particle has an unbounded growth of the MSD in time, with no signatures of localization. In the case of projective measurements at random times, we show that repeated projection to the initial state of the particle results in an effective suppression of the temporal decay in the probability of the particle to be found on the initial state. The amount of suppression is comparable to the one in conventional Zeno effect scenarios, but which it does not require us to perform measurements at exactly regular intervals that are hallmarks of such scenarios.
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NAKAZATO, HIROMICHI, MIKIO NAMIKI et SAVERIO PASCAZIO. « TEMPORAL BEHAVIOR OF QUANTUM MECHANICAL SYSTEMS ». International Journal of Modern Physics B 10, no 03 (30 janvier 1996) : 247–95. http://dx.doi.org/10.1142/s0217979296000118.
Texte intégralRésumé :
The temporal behavior of quantum mechanical systems is reviewed. We mainly focus our attention on the time development of the so-called “survival” probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by assuming that the latter has a continuous spectrum. The exponential decay of the survival probability, familiar, for example, in radioactive decay phenomena, is representative of a purely probabilistic character of the system under consideration and is naturally expected to lead to a master equation. This behavior, however, can be found only at intermediate times, for deviations from it exist both at short and long times and can have significant consequences. After a short introduction to the long history of the research on the temporal behavior of such quantum mechanical systems, the short-time behavior and its controversial consequences when it is combined with von Neumann’s projection postulate in quantum measurement theory are critically overviewed from a dynamical point of view. We also discuss the so-called quantum Zeno effect from this standpoint. The behavior of the survival amplitude is then scrutinized by investigating the analytic properties of its Fourier and Laplace transforms. The analytic property that there is no singularity except a branch cut running along the real energy axis in the first Riemannian sheet is an important reflection of the time-reversal invariance of the dynamics governing the whole process. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter. In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system, since the exponential behavior is regarded as a manifestation of a complete loss of coherence of the quantum subsystem under consideration. In this respect, a few attempts at extracting the exponential decay form on the basis of quantum theory, aiming at the master equation, are briefly reviewed, including van Hove’s pioneering work and his well-known “λ2T” limit. In the attempt to further clarify the mechanism of the appearance of a purely probabilistic behavior without resort to any approximation, a solvable dynamical model is presented and extensively studied. The model describes an ultrarelativistic particle interacting with N two-level systems (called “spins”) and is shown to exhibit an exponential behavior at all times in the weak-coupling, macroscopic limit. Furthermore, it is shown that the model can even reproduce the short-time Gaussian behavior followed by the exponential law when an appropriate initial state is chosen. The analysis is exact and no approximation is involved. An interpretation for the change of the temporal behavior in quantum systems is drawn from the results obtained. Some implications for the quantum measurement problem are also discussed, in particular in connection with dissipation.
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Anggoro, Bambang Sri. « Sejarah Teori Peluang dan Statistika ». Al-Jabar : Jurnal Pendidikan Matematika 6, no 1 (16 juin 2015) : 13–24. http://dx.doi.org/10.24042/ajpm.v6i1.55.
Texte intégralRésumé :
Opportunity theory is a branch of mathematics concerned with opportunities, analysis of random phenomena. The main objects of opportunity theory are random variables, stochastic processes, and events: a non-deterministic mathematical abstraction of measurable events or quantities that can be either single events or develop over time in seemingly random modes. If individual coins throw or dice rolls are considered random events, then if repeated sequences of random events will show certain patterns, which can be learned and predicted. Two representative mathematical results illustrating such patterns are the laws of large numbers and the central limit theorem. As a mathematical basis for statistics, probability theory is important for many human activities that involve quantitative analysis of large sets of data. The method of opportunity theory also applies to complex system descriptions given only partial knowledge of their country, as in statistical mechanics. A great discovery of twentieth-century physics is the nature of probability of physical phenomena on the atomic scale, described in quantum mechanics.
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Castorina, Paolo, Alfredo Iorio et Helmut Satz. « Hunting Quantum Gravity with Analogs : The Case of High-Energy Particle Physics ». Universe 8, no 9 (13 septembre 2022) : 482. http://dx.doi.org/10.3390/universe8090482.
Texte intégralRésumé :
In this review, we collect, for the first time, old and new research results, and present future perspectives on how hadron production, in high-energy scattering processes, can experimentally probe fundamental questions of quantum gravity. The key observations that ignited the link between the two arenas are the so-called “color-event horizon” of quantum chromodynamics, and the (de)accelerations involved in such scattering processes. Both phenomena point to the Unruh (and related Hawking)-type effects. After the first pioneering investigations, such research studies continued, including studies of the horizon entropy and other “black-hole thermodynamical” behaviors, which incidentally are also part of the frontier of the analog gravity research itself. It has been stressed that the trait d’union between the two phenomenologies is that in both hadron physics and black hole physics, “thermal” behaviors are more easily understood, not as due to real thermalization processes (sometimes just impossible, given the small number of particles involved), but rather to a stochastic/quantum entanglement nature of such temperatures. Finally, other aspects, such as the self-critical organizations of hadronic matter and of black holes, have been recently investigated. The results of those investigations are also summarized and commented upon here. As a general remark, this research line shows that we can probe quantum gravity theoretical constructions with analog systems that are not confined to only the condensed matter arena.
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Montina, Alberto. « Communication complexity and the reality of the wave function ». Modern Physics Letters A 30, no 01 (7 janvier 2015) : 1530001. http://dx.doi.org/10.1142/s0217732315300013.
Texte intégralRésumé :
In this review, we discuss a relation between quantum communication complexity and a long-standing debate in quantum foundation concerning the interpretation of the quantum state. Is the quantum state a physical element of reality as originally interpreted by Schrödinger? Or is it an abstract mathematical object containing statistical information about the outcome of measurements as interpreted by Born? Although these questions sound philosophical and pointless, they can be made precise in the framework of what we call classical theories of quantum processes, which are a reword of quantum phenomena in the language of classical probability theory. In 2012, Pusey, Barrett and Rudolph (PBR) proved, under an assumption of preparation independence, a theorem supporting the original interpretation of Schrödinger in the classical framework. The PBR theorem has attracted considerable interest revitalizing the debate and motivating other proofs with alternative hypotheses. Recently, we showed that these questions are related to a practical problem in quantum communication complexity, namely, quantifying the minimal amount of classical communication required in the classical simulation of a two-party quantum communication process. In particular, we argued that the statement of the PBR theorem can be proved if the classical communication cost of simulating the communication of n qubits grows more than exponentially in n. Our argument is based on an assumption that we call probability equipartition property. This property is somehow weaker than the preparation independence property used in the PBR theorem, as the former can be justified by the latter and the asymptotic equipartition property of independent stochastic sources. The probability equipartition property is a general and natural hypothesis that can be assumed even if the preparation independence hypothesis is dropped. In this review, we further develop our argument into the form of a theorem.
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Yudenkov, A. V., A. M. Volodchenkov et L. P. Rimskaya. « SIMULATION OF RADIATION IN MICROSYSTEMS USING MARKOV CHAINS ». T-Comm 16, no 10 (2022) : 12–18. http://dx.doi.org/10.36724/2072-8735-2022-16-10-12-18.
Texte intégralRésumé :
To solve important problems related to radiation in microsystems, the methods of quantum electrodynamics are successfully used. At the same time, a number of problems remain (vacuum energy, divergence in local interaction, the physical meaning of the fine structure constant) that cannot be resolved within the framework of this theory. Therefore, an urgent task is to develop alternative mathematical models that can be additionally used to study the radiation process in microsystems. In this work, to model the radiation process in microsystems, Markov processes with continuous time and discrete states are used. The mathematical model is based on Heisenberg's uncertainty principles and conservation laws. The main mathematical tools are Kolmogorov graphs and their corresponding systems of equations. The key idea is that the phase space of a particle is discrete. The model of the discrete phase space is distinguished by its comparative simplicity and efficiency, and allows applying the well-developed theory of Markov processes to the phenomena under study. The scale of the model and its discrete structure make it possible to avoid irremovable singularities. The article presents: an original physical interpretation of the fine structure constant, a stochastic analogue of the redshift law and the magnitude of the Schwarzschild gravitational radius, a stochastic interpretation of the fine structure constant of the gravitational field is proposed. A comparative analysis of the fine structure constants for the gravitational and electromagnetic fields has been carried out.
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Tsuruta, Kenij, Atsushi Uchida, Chieko Totsuji et Hiroo Totsuji. « Multiscale Molecular Dynamics Simulations of Nanostructured Materials ». Materials Science Forum 539-543 (mars 2007) : 2804–9. http://dx.doi.org/10.4028/www.scientific.net/msf.539-543.2804.
Texte intégralRésumé :
We present some attempts to simulate nanoscale phenomena, which involve different length-scales and time-scales, using multiscale molecular-dynamics approaches. To simulate realistically an impurity-segregated nanostructure, we have developed the hybrid quantum/classical approach. The method can describe seamlessly both dynamical changes of local chemical bonding and nanoscale atomic relaxations. We apply the method to hydrogen diffusion in Si grain boundary. We find that the hydrogen is strongly trapped in (001)Σ5 twist boundary below 1000K, whereas it starts diffusing along the grain boundary above 1000K. For long-time processes in nanostructure formation, we apply the stochastic-difference-equation method to accelerate the simulations for microstructure evolution. The method bridges the states separated by high-energy barriers in a configuration space by optimizing an action, defined as an error accumulation along a reaction pathway. As an example, a SDE simulation is performed for Cu thin-film formation via nanocluster deposition. We show that the method can be applied effectively to search for the long-time process which involves a rare event due to a large potential barrier between two atomic configurations.