Artigos de revistas: "Gaussian quantum mechanics"

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ACOSTA, D., P. FERNÁNDEZ DE CÓRDOBA, J. M. ISIDRO e J. L. G. SANTANDER. "EMERGENT QUANTUM MECHANICS AS A CLASSICAL, IRREVERSIBLE THERMODYNAMICS". International Journal of Geometric Methods in Modern Physics 10, n.º 04 (6 de março de 2013): 1350007. http://dx.doi.org/10.1142/s0219887813500072.

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We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e. an effective description of some underlying degrees of freedom.

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Sankovich, D. P. "Bogolyubov Gaussian Measure in Quantum Statistical Mechanics". Universal Journal of Physics and Application 13, n.º 2 (março de 2019): 29–41. http://dx.doi.org/10.13189/ujpa.2019.130201.

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Simon, R., E. C. G. Sudarshan e N. Mukunda. "Gaussian-Wigner distributions in quantum mechanics and optics". Physical Review A 36, n.º 8 (1 de outubro de 1987): 3868–80. http://dx.doi.org/10.1103/physreva.36.3868.

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KHRENNIKOV, ANDREI. "QUANTUM CORRELATIONS FROM CLASSICAL GAUSSIAN RANDOM VARIABLES: FUNDAMENTAL ROLE OF VACUUM NOISE". Fluctuation and Noise Letters 09, n.º 04 (dezembro de 2010): 331–41. http://dx.doi.org/10.1142/s0219477510000265.

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We show that, in spite of rather common opinion, correlations of observables on subsystems of a composite quantum system can be represented as correlations of classical Gaussian variables. We restrict our model to the finite dimensional case (which is important, e.g., in quantum information theory). Here quantum correlations are represented by integrals with Gaussian densities which can be directly calculated. In particular, the EPR–Bell correlations for polarizations of entangled photons can be represented as correlations of Gaussian random variables. The tricky point of our construction is the necessity to introduce the Gaussian noise ("vacuum fluctuations") to obtain positively defined covariance matrices for "prequantum random variables." Quantum mechanics can be considered as a method to proceed by subtracting the influence of this Gaussian background noise.

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Przhiyalkovskiy, Y. V. "Quantum process in probability representation of quantum mechanics". Journal of Physics A: Mathematical and Theoretical 55, n.º 8 (1 de fevereiro de 2022): 085301. http://dx.doi.org/10.1088/1751-8121/ac4b15.

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Abstract In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving of which with the initial tomogram set characterizing the system state gives the tomographic state of the transformed system. This kernel, in turn, is broken into the kernels of partial operations, each of them incorporating the symbol of the evolution operator related to the joint evolution of the system and an ancillary environment. Such a kernel decomposition for the projection to a certain basis state and a Gaussian-type projection is demonstrated as well as qubit flipping and amplitude damping processes.

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ALAVI, S. A. "SCATTERING IN NONCOMMUTATIVE QUANTUM MECHANICS". Modern Physics Letters A 20, n.º 13 (30 de abril de 2005): 1013–20. http://dx.doi.org/10.1142/s021773230501697x.

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We derive the correction due to noncommutativity of space on Born approximation, then the correction for the case of Yukawa potential is explicitly calculated. The correction depends on the angle of scattering. Using partial wave method, it is shown that the conservation of the number of particles in elastic scattering is also valid in noncommutative spaces which means that the unitarity relation is held in noncommutative spaces. We also show that the noncommutativity of space has no effect on the optical theorem. Finally we study Gaussian function potential in noncommutative spaces which generates delta function potential as θ → 0.

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Iomin, Alexander, Ralf Metzler e Trifce Sandev. "Topological Subordination in Quantum Mechanics". Fractal and Fractional 7, n.º 6 (25 de maio de 2023): 431. http://dx.doi.org/10.3390/fractalfract7060431.

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An example of non-Markovian quantum dynamics is considered in the framework of a geometrical (topological) subordination approach. The specific property of the model is that it coincides exactly with the fractional diffusion equation, which describes the geometric Brownian motion on combs. Both classical diffusion and quantum dynamics are described using the dilatation operator xddx. Two examples of geometrical subordinators are considered. The first one is the Gaussian function, which is due to the comb geometry. For the quantum consideration with a specific choice of the initial conditions, it corresponds to the integral representation of the Mittag–Leffler function by means of the subordination integral. The second subordinator is the Dirac delta function, which results from the memory kernels that define the fractional time derivatives in the fractional diffusion equation.

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Schnabel, Roman, e Mikhail Korobko. "Macroscopic quantum mechanics in gravitational-wave observatories and beyond". AVS Quantum Science 4, n.º 1 (março de 2022): 014701. http://dx.doi.org/10.1116/5.0077548.

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The existence of quantum correlations affects both microscopic and macroscopic systems. On macroscopic systems, they are difficult to observe and usually irrelevant for the system's evolution due to the frequent energy exchange with the environment. The world-wide network of gravitational-wave (GW) observatories exploits optical as well as mechanical systems that are highly macroscopic and largely decoupled from the environment. The quasi-monochromatic light fields in the kilometer-scale arm resonators have photon excitation numbers larger than 1019, and the mirrors that are quasi-free falling in propagation direction of the light fields have masses of around 40 kg. Recent observations on the GW observatories LIGO and Virgo clearly showed that the quantum uncertainty of one system affected the uncertainty of the other. Here, we review these observations and provide links to research goals targeted with mesoscopic optomechanical systems in other fields of fundamental physical research. These may have Gaussian quantum uncertainties as the ones in GW observatories or even non-Gaussian ones, such as Schrödinger cat states.

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MUÑOZ-TAPIA, R., J. TARON e R. TARRACH. "THE UNCERTAINTY OF THE GAUSSIAN EFFECTIVE POTENTIAL". International Journal of Modern Physics A 03, n.º 09 (setembro de 1988): 2143–63. http://dx.doi.org/10.1142/s0217751x88000898.

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An uncertainty is introduced for the Gaussian Effective Potential. The definition is quite straightforward for quantum mechanics but fairly subtle for quantum field theory. The uncertainty provides a good estimation of the error in the first case, but renormalization seems to spoil its usefulness in the second case. The examples considered are the anharmonic oscillator, λϕ4 in 3+1 dimensions and the Liouville theory in 1+1 dimensions.

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Lasser, Caroline, e Christian Lubich. "Computing quantum dynamics in the semiclassical regime". Acta Numerica 29 (maio de 2020): 229–401. http://dx.doi.org/10.1017/s0962492920000033.

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The semiclassically scaled time-dependent multi-particle Schrödinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This paper reviews and studies numerical approaches that are robust to the small semiclassical parameter. We present and analyse variationally evolving Gaussian wave packets, Hagedorn’s semiclassical wave packets, continuous superpositions of both thawed and frozen Gaussians, and Wigner function approaches to the direct computation of expectation values of observables. Making good use of classical mechanics is essential for all these approaches. The arising aspects of time integration and high-dimensional quadrature are also discussed.

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Nauenberg, Michael. "Quantum Mechanics and Liouville's Equation". Quanta 6, n.º 1 (9 de setembro de 2017): 53. http://dx.doi.org/10.12743/quanta.v6i1.63.

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In non-relativistic quantum mechanics, the absolute square of Schrödinger's wave function for a particle in a potential determines the probability of finding it either at a position or momentum at a given time. In classical mechanics the corresponding problem is determined by the solution of Liouville's equation for the probability density of finding the joint position and momentum of the particle at a given time. Integrating this classical solution over either one of these two variables can then be compared with the probability in quantum mechanics. For the special case that the force is a constant, it is shown analytically that for an initial Gaussian probability distribution, the solution of Liouville's integrated over momentum is equal to Schrödinger's probability function in coordinate space, provided the coordinate and momentum initial widths of this classical solution satisfy the minimal Heisenberg uncertainty relation. Likewise, integrating Lioville's solution over position is equal to Schrödinger's probability function in momentum space.Quanta 2017; 6: 53–56.

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Schönhammer, K. "Quantum versus classical quenches and the broadening of wave packets". American Journal of Physics 92, n.º 6 (1 de junho de 2024): 466–72. http://dx.doi.org/10.1119/5.0174441.

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The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed, but a comparison with results for the dynamics in the framework of classical statistical mechanics is useful. Analytical results are presented when the initial and final potentials are harmonic oscillators. When the final potential vanishes, the problem reduces to the broadening of wave packets. A simple introduction to the concept of the Wigner function is presented, which allows a better understanding of the dynamics of general wave packets. It is pointed out how special the broadening of Gaussian wave packets is, the only example usually presented in quantum mechanics textbooks.

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Simon, R., E. C. G. Sudarshan e N. Mukunda. "Gaussian pure states in quantum mechanics and the symplectic group". Physical Review A 37, n.º 8 (1 de abril de 1988): 3028–38. http://dx.doi.org/10.1103/physreva.37.3028.

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Buividovich, Pavel, Masanori Hanada e Andreas Schäfer. "Real-time dynamics of matrix quantum mechanics beyond the classical approximation". EPJ Web of Conferences 175 (2018): 08006. http://dx.doi.org/10.1051/epjconf/201817508006.

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We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

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Hosseini, Reza, Samin Tajik, Zahra Koohi Lai, Tayeb Jamali, Emmanuel Haven e Reza Jafari. "Quantum Bohmian-Inspired Potential to Model Non–Gaussian Time Series and Its Application in Financial Markets". Entropy 25, n.º 7 (14 de julho de 2023): 1061. http://dx.doi.org/10.3390/e25071061.

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We have implemented quantum modeling mainly based on Bohmian mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study was to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ, which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying the quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case.

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Rybakov, Yu P. "RANDOM HILBERT SPACE AND WIENER’S INTERPRETATION OF QUANTUM MECHANICS". Metaphysics, n.º 2 (15 de dezembro de 2023): 76–80. http://dx.doi.org/10.22363/2224-7580-2023-2-76-80.

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The special representation of quantum mechanics suggested by Wiener is studied, the wave function being considered as Gaussian random variable, i. e. the vector of the random Hilbert space. The connection between this representation and the well-known Einstein’s program aiming at creating the consistent field formulation of particle physics is revealed, with particles being represented as solitons, clots of some material field satisfying nonlinear equations.

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Bonet-Luz, Esther, e Cesare Tronci. "Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, n.º 2189 (maio de 2016): 20150777. http://dx.doi.org/10.1098/rspa.2015.0777.

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The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest’s theorem is shown to be Lie–Poisson for a semidirect-product Lie group, named the Ehrenfest group . The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie–Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature.

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Borges, O. N., e L. A. Amarante Ribeiro. "Statistical mechanics of quantum one-dimensional damped harmonic oscillators: II". Canadian Journal of Physics 65, n.º 7 (1 de julho de 1987): 715–18. http://dx.doi.org/10.1139/p87-104.

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We show that the Caldirola–Kanai Hamiltonian of the one-dimensional damped oscillator describes in a specified basis a Gaussian, Markoffian process, in the weak coupling limit. We also discuss which assumption makes the process stationary and clarify the relationship with the master-equation approach.

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Stepanyan, V., e A. E. Allahverdyan. "Energy densities in quantum mechanics". Quantum 8 (10 de janeiro de 2024): 1223. http://dx.doi.org/10.22331/q-2024-01-10-1223.

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Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic description for a spin-12 particle: Dirac's equation. Employing its energy-momentum tensor and going to the non-relativistic limit we find a locally conserved non-relativistic energy density that is defined via the Terletsky-Margenau-Hill quasiprobability (which is hence selected among other options). It coincides with the weak value of energy, and also with the hydrodynamic energy in the Madelung representation of quantum dynamics, which includes the quantum potential. Moreover, we find a new form of spin-related energy that is finite in the non-relativistic limit, emerges from the rest energy, and is (separately) locally conserved, though it does not contribute to the global energy budget. This form of energy has a holographic character, i.e., its value for a given volume is expressed via the surface of this volume. Our results apply to situations where local energy representation is essential; e.g. we show that the energy transfer velocity for a large class of free wave-packets (including Gaussian and Airy wave-packets) is larger than its group (i.e. coordinate-transfer) velocity.

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Pastorello, Davide. "A geometrization of quantum mutual information". International Journal of Quantum Information 17, n.º 02 (março de 2019): 1950011. http://dx.doi.org/10.1142/s0219749919500114.

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It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kähler manifold. In this paper, we consider the notion of mutual information among continuous random variables in relation to the geometric description of a composite quantum system introducing a new measure of total correlations that can be computed in terms of Gaussian integrals.

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Kryukov, Alexey A. "The measurement in classical and quantum theory". Journal of Physics: Conference Series 2482, n.º 1 (1 de maio de 2023): 012025. http://dx.doi.org/10.1088/1742-6596/2482/1/012025.

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Abstract The Bohigas-Giannoni-Schmit (BGS) conjecture states that the Hamiltonian of a microscopic analogue of a classical chaotic system can be modeled by a random matrix from a Gaussian ensemble. Here, this conjecture is considered in the context of a recently discovered geometric relationship between classical and quantum mechanics. Motivated by BGS, we conjecture that the Hamiltonian of a system whose classical counterpart performs a random walk can be modeled by a family of independent random matrices from the Gaussian unitary ensemble. By accepting this conjecture, we find a relationship between the process of observation in classical and quantum physics, derive irreversibility of observation and describe the boundary between the micro and macro worlds.

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Schulman, Lawrence S. "Causality Is an Effect, II". Entropy 23, n.º 6 (28 de maio de 2021): 682. http://dx.doi.org/10.3390/e23060682.

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Causality follows the thermodynamic arrow of time, where the latter is defined by the direction of entropy increase. After a brief review of an earlier version of this article, rooted in classical mechanics, we give a quantum generalization of the results. The quantum proofs are limited to a gas of Gaussian wave packets.

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Choi, Jeong Ryeol, e Ji Nny Song. "Quantum Analysis on Time Behavior of a Lengthening Pendulum". Physics Research International 2016 (3 de fevereiro de 2016): 1–9. http://dx.doi.org/10.1155/2016/1696105.

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Quantum properties of a lengthening pendulum are studied under the assumption that the length of the string increases at a steady rate. Advanced analysis for various physical problems in several types of quantum states, such as propagators, Wigner distribution functions, energy eigenvalues, probability densities, and dispersions of physical quantities, is carried out using quantum wave functions of the system. In particular, the time behavior of Gaussian-type wave packets is investigated in detail. The probability density for a Gaussian wave packet displaced in the positive θ at t=0 oscillates back and forth from the center (θ=0). This phenomenon is very similar to the classical motion of the pendulum. As a consequence, we can confirm that there is a correspondence between its quantum and classical behaviors. When we analyze a dynamical system in view of quantum mechanics, the quantum and classical correspondence is very important in order for the associated quantum theory to be valid and viable.

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Hicks, Will. "PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black–Scholes Equation". Entropy 21, n.º 2 (23 de janeiro de 2019): 105. http://dx.doi.org/10.3390/e21020105.

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The Accardi–Boukas quantum Black–Scholes framework, provides a means by which one can apply the Hudson–Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via a Kramers–Moyal expansion, and this provides useful tools to understand their behaviour. In this paper we develop further links between quantum stochastic processes, and nonlocal diffusions, by inverting the question, and showing how certain nonlocal diffusions can be written as quantum stochastic processes. We then go on to show how one can use path integral formalism, and PT symmetric quantum mechanics, to build a non-Gaussian kernel function for the Accardi–Boukas quantum Black–Scholes. Behaviours observed in the real market are a natural model output, rather than something that must be deliberately included.

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Maksic, Z. B., K. Kovacevic e M. Primorac. "New basis sets in quantum mechanics of molecules: Hermite-Gaussian functions". Pure and Applied Chemistry 61, n.º 12 (1 de janeiro de 1989): 2075–85. http://dx.doi.org/10.1351/pac198961122075.

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Accardi, Luigi. "New Challenges for Classical and Quantum Probability". Entropy 24, n.º 10 (21 de outubro de 2022): 1502. http://dx.doi.org/10.3390/e24101502.

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The discovery that any classical random variable with all moments gives rise to a full quantum theory (that in the Gaussian and Poisson cases coincides with the usual one) implies that a quantum–type formalism will enter into practically all applications of classical probability and statistics. The new challenge consists in finding the classical interpretation, for different types of classical contexts, of typical quantum notions such as entanglement, normal order, equilibrium states, etc. As an example, every classical symmetric random variable has a canonically associated conjugate momentum. In usual quantum mechanics (associated with Gaussian or Poisson classical random variables), the interpretation of the momentum operator was already clear to Heisenberg. How should we interpret the conjugate momentum operator associated with classical random variables outside the Gauss–Poisson class? The Introduction is intended to place in historical perspective the recent developments that are the main object of the present exposition.

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Ningsih P. A. Sunaryo, Ayu, Herry F. Lalus e Hartoyo Yudhawardana. "ANALISIS FUNGSI KORELASI KLASIK DAN KUANTUM UNTUK MODEL CINCIN: SEBUAH REVIEW". JOURNAL ONLINE OF PHYSICS 9, n.º 1 (2 de novembro de 2023): 36–42. http://dx.doi.org/10.22437/jop.v9i1.27501.

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A review of the journal entitled 'Classical And Quantum Correlation Functions For A Ring Model' has been carried out which discusses the solutions of classical and quantum correlation functions for the ring model. Classical and quantum correlation functions are derived for systems of non-interacting particles moving in a circle. demonstrated that the decay behavior of the classical expression for the correlation function can be recovered from a strictly periodic quantum mechanical expression by taking the limit ℏ→0, after the appropriate transformation. The aim of this study is to present clearly and in detail how the position correlation function for a system of particles moving in a circle having a certain average energy and written in a form which shows the nature of the transformation. Next, we examine the use of Poisson addition to represent F(z), and how the correlation function becomes identical to the form given by classical statistical mechanics, which exhibits Gaussian decay. The results of this study indicate that the positional correlation function for a system of particles moving in a circle, and having a certain average energy, can be written in a form which shows the nature of the transformation. Then using the Poisson addition formula to represent F(z), the expression is rewritten to enable the limit ℏ→0 to be taken. It was finally found that the correlation function became identical to the form given by classical statistical mechanics, which exhibits a Gaussian decay.

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Huang, Wayne Cheng-Wei, e Herman Batelaan. "Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation". Journal of Computational Methods in Physics 2013 (7 de outubro de 2013): 1–19. http://dx.doi.org/10.1155/2013/308538.

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Stochastic electrodynamics (SED) predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.

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Lahlou, Y., M. Amazioug, J. El Qars, N. Habiballah, M. Daoud e M. Nassik. "Quantum coherence versus nonclassical correlations in optomechanics". International Journal of Modern Physics B 33, n.º 29 (20 de novembro de 2019): 1950343. http://dx.doi.org/10.1142/s0217979219503430.

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Coherence arises from the superposition principle, where it plays a central role in quantum mechanics. In Phys. Rev. Lett. 114, 210401 (2015), it has been shown that the freezing phenomenon of quantum correlations beyond entanglement is intimately related to the freezing of quantum coherence (QC). In this paper, we compare the behavior of entanglement and quantum discord with quantum coherence in two different subsystems (optical and mechanical). We use respectively the entanglement of formation (EoF) and the Gaussian quantum discord (GQD) to quantify entanglement and quantum discord. Under thermal noise and optomechanical coupling effects, we show that EoF, GQD and QC behave in the same way. Remarkably, when entanglement vanishes, GQD and QC remain almost unaffected by thermal noise, keeping nonzero values even for high-temperature, which is in concordance with Phys. Rev. Lett. 114, 210401 (2015). Also, we find that the coherence associated with the optical subsystem is more robust — against thermal noise — than those of the mechanical subsystem. Our results confirm that optomechanical cavities constitute a powerful resource of QC.

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Zengel, Keith, Nick DeVitto, Nathanael Hillyer, Jeffrey Rodden e Vinh Vu. "The uncertainty principle and quantum wave functions that are their own Fourier transforms". American Journal of Physics 92, n.º 3 (1 de março de 2024): 189–96. http://dx.doi.org/10.1119/5.0162363.

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We present several variations of a proof of the position-momentum uncertainty principle that are based on the calculus of variations and does not rely on the Cauchy–Schwartz inequality. We show that the stationary uncertainty wave functions are the Hermite–Gaussian solutions to the quantum harmonic oscillator problem, that the minimum uncertainty wave function is the Gaussian, and that stationary uncertainty wave functions must be their own Fourier transforms. We also provide a calculus of variations proof of the Cauchy–Schwartz inequality. Finally, we discuss the properties of wave functions that are their own Fourier transforms and provide examples of such functions that may be of interest to teachers of undergraduate and graduate level quantum mechanics courses.

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Mizrahi, S. S. "Quantum mechanics in the Gaussian wave-packet phase space representation II: Dynamics". Physica A: Statistical Mechanics and its Applications 135, n.º 1 (março de 1986): 237–50. http://dx.doi.org/10.1016/0378-4371(86)90115-9.

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Epperson, Michael. "Quantum Mechanics and Relational Realism: Logical Causality and Wave Function Collapse". Process Studies 38, n.º 2 (1 de outubro de 2009): 340–67. http://dx.doi.org/10.2307/44798493.

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Abstract By the relational realist interpretation of wave function collapse, the quantum mechanical actualization of potentia is defined as a decoherence-driven process by which each actualization (in "orthodox" terms, each measurement outcome) is conditioned both by physical ana logical relations with the actualities conventionally demarked as "environmental" or external to that particular outcome. But by the relational realist interpretation, the actualization-in-process is understood as internally related to these "enironmental" data per the formalism of quantum decoherence. The concept of "actualization via wave function collapse" is accounted for solely by virtue of these presupposed logical relations—the same logical relations otherwise presupposed by the scientific method itself—and thus requires no "external" physical-dynamical trigger: e.g., the Gaussian hits of GRW, acts of conscious observation, etc. By the relational realist interpretation, it is the physical and logical relations among quantum actualities (quantum "final real things") that drives the process of decoherence and, via the latter, the logically conditioned actualization of potentia. In this regard, the relational realist interpretation of quantum mechanics is a praxiological interpretation; that is, these physical and logical relations are ontobgically active relations, contributing not just to the epistemic coordination of quantum actualizations, but to the process of actualization itself.

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Xu, Aidong, Wenqi Huang, Peng Li, Huajun Chen, Jiaxiao Meng e Xiaobin Guo. "Mechanical Vibration Signal Denoising Using Quantum-Inspired Standard Deviation Based on Subband Based Gaussian Mixture Model". Shock and Vibration 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/5169070.

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Aiming at improving noise reduction effect for mechanical vibration signal, a Gaussian mixture model (SGMM) and a quantum-inspired standard deviation (QSD) are proposed and applied to the denoising method using the thresholding function in wavelet domain. Firstly, the SGMM is presented and utilized as a local distribution to approximate the wavelet coefficients distribution in each subband. Then, within Bayesian framework, the maximum a posteriori (MAP) estimator is employed to derive a thresholding function with conventional standard deviation (CSD) which is calculated by the expectation-maximization (EM) algorithm. However, the CSD has a disadvantage of ignoring the interscale dependency between wavelet coefficients. Considering this limit for the CSD, the quantum theory is adopted to analyze the interscale dependency between coefficients in adjacent subbands, and the QSD for noise-free wavelet coefficients is presented based on quantum mechanics. Next, the QSD is constituted for the CSD in the thresholding function to shrink noisy coefficients. Finally, an application in the mechanical vibration signal processing is used to illustrate the denoising technique. The experimental study shows the SGMM can model the distribution of wavelet coefficients accurately and QSD can depict interscale dependency of wavelet coefficients of true signal quite successfully. Therefore, the denoising method utilizing the SGMM and QSD performs better than others.

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Haapasalo, Erkka, Tristan Kraft, Nikolai Miklin e Roope Uola. "Quantum marginal problem and incompatibility". Quantum 5 (15 de junho de 2021): 476. http://dx.doi.org/10.22331/q-2021-06-15-476.

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One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even higher order dynamics. In this manuscript, we show that two seemingly different aspects of quantum incompatibility: the quantum marginal problem of states and the incompatibility on the level of quantum channels are in many-to-one correspondence. Importantly, as incompatibility of measurements is a special case of the latter, it also forms an instance of the quantum marginal problem. The generality of the connection is harnessed by solving the marginal problem for Gaussian and Bell diagonal states, as well as for pure states under depolarizing noise. Furthermore, we derive entropic criteria for channel compatibility, and develop a converging hierarchy of semi-definite programs for quantifying the strength of quantum memories.

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Silva, L. D. da, J. L. L. dos Santos, A. Ranciaro Neto, M. O. Sales e F. A. B. F. de Moura. "One-electron propagation in Fermi, Pasta, Ulam disordered chains with Gaussian acoustic pulse pumping". International Journal of Modern Physics C 28, n.º 08 (agosto de 2017): 1750100. http://dx.doi.org/10.1142/s0129183117501005.

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In this work, we consider a one-electron moving on a Fermi, Pasta, Ulam disordered chain under effect of electron–phonon interaction and a Gaussian acoustic pulse pumping. We describe electronic dynamics using quantum mechanics formalism and the nonlinear atomic vibrations using standard classical physics. Solving numerical equations related to coupled quantum/classical behavior of this system, we study electronic propagation properties. Our calculations suggest that the acoustic pumping associated with the electron–lattice interaction promote a sub-diffusive electronic dynamics.

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AGARWAL, ABHISHEK. "MASS DEFORMATIONS OF SUPER YANG–MILLS THEORIES IN D = 2 + 1, AND SUPER-MEMBRANES: A NOTE". Modern Physics Letters A 24, n.º 03 (30 de janeiro de 2009): 193–211. http://dx.doi.org/10.1142/s0217732309028904.

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Mass deformations of supersymmetric Yang–Mills theories in three spacetime dimensions are considered. The gluons of the theories are made massive by the inclusion of a nonlocal gauge and Poincaré invariant mass term due to Alexanian and Nair, while the matter fields are given standard Gaussian mass-terms. It is shown that the dimensional reduction of such mass-deformed gauge theories defined on R3 or R × T2 produces matrix quantum mechanics with massive spectra. In particular, all known massive matrix quantum mechanical models obtained by the deformations of dimensional reductions of minimal super Yang–Mills theories in diverse dimensions are shown also to arise from the dimensional reductions of appropriate massive Yang–Mills theories in three spacetime dimensions. Explicit formulas for the gauge theory actions are provided.

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Jusufi, Kimet. "Quantum effects on the deflection of light and the Gauss–Bonnet theorem". International Journal of Geometric Methods in Modern Physics 14, n.º 10 (13 de setembro de 2017): 1750137. http://dx.doi.org/10.1142/s0219887817501377.

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In this paper, we apply the Gauss–Bonnet (GB) theorem to calculate the deflection angle by a quantum-corrected Schwarzschild black hole in the weak limit approximation. In particular, we calculate the light deflection by two types of quantum-corrected black holes: the renormalization group improved Schwarzschild solution and the quantum-corrected Schwarzschild solution in Bohmian quantum mechanics. We start from the corresponding optical metrics to use then the GB theorem and calculate the Gaussian curvature in both cases. We calculate the leading terms of the deflection angle and show that quantum corrections modify the deflection angle in both solutions. Finally by performing geodesics calculations we show that GB method gives exact results in leading-order terms.

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Maignan, Aude, e Tony Scott. "A Comprehensive Analysis of Quantum Clustering : Finding All the Potential Minima". International Journal of Data Mining & Knowledge Management Process 11, n.º 1 (31 de janeiro de 2021): 33–54. http://dx.doi.org/10.5121/ijdkp.2021.11103.

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Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a σ value, a hyper-parameter which can be manually defined and manipulated to suit the application. Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an outstanding task because normally such expressions are impossible to solve analytically. However, we prove that if the points are all included in a square region of size σ, there is only one minimum. This bound is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new numerical approach “per block”. This technique decreases the number of particles by approximating some groups of particles to weighted particles. These findings are not only useful to the quantum clustering problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics and other applications.

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Snider, R. F. "Eigenvalues and eigenvectors for a hermitian gaussian operator: Role of the Schrödinger-Robertson uncertainty relation". Electronic Research Archive 31, n.º 9 (2023): 5541–58. http://dx.doi.org/10.3934/era.2023281.

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<abstract><p>The eigenvalues and eigenvectors of a normalized gaussian operator do not seem to have been previously considered. I solve this problem for 1-dimensional translational systems. I also address the question as to whether a gaussian operator is a density operator. To answer that question, it is first necessary to be sure what conditions must be satisfied, so a short review of density operators is given. Since position and momentum do not commute in quantum mechanics, it is useful to start with the consequences of the noncommutation, which is generally the Schrödinger-Robertson uncertainty relation, which is also briefly reviewed. It is found that the question of whether a gaussian operator is a density operator is directly tied to this uncertainty relation. Since the Wigner function is the phase space representation of a translational density operator, it is natural to consider the gaussian phase space function associated with a gaussian operator and to compare the phase space and operator properties. Throughout such discussions, the independent parameters in these functions are the first and second moments of position and momentum. The application of this formalism to the free translation and spreading of a gaussian packet is given and shows the formal similarity between classical and quantum behavior, whereas the literature standardly only considers the pure state case (equivalent to a single wavefunction).</p></abstract>

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40

Al-Hyali, Emad A. S., e Yosef Othman Al-Jobure. "Calculation of the Chemical Shift of N-15 by Quantum Mechanics". International Journal of Biological, Physical and Chemical Studies 4, n.º 2 (22 de novembro de 2022): 43–53. http://dx.doi.org/10.32996/ijbpcs.2022.4.2.5.

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This study aims to develop a new set of added variables to calculate the chemical shift N-15 based on quantum mechanics methods for a number of periodic compounds using theoretical chemistry (Gaussian V.12, 2010). The relationship between the experimental N-15 was conducted with two mechanical variables, such as SPSS V 2019. The relationship between the theoretical chemical shift values of the N-15 atom nucleus and practical values in literature was examined. Two quantitative mechanical methods are used to extract information to calculate the N-15 chemical shift, the traditional method, the other AB Initio method, and the DFT job theory. The success of the method is determined in terms of the values of the correlation coefficient (R) and the standard error (SE), as well as the material meaning of the specified variables. A good consensus is seen between practical and theoretical values. A comparison was made between the two methods to find out the best in the chemical transformation account. The DFT method gave better results.

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Khorrami, Mohammad. "Position, momentum, and wave spreading in curved space". International Journal of Modern Physics A 36, n.º 08n09 (30 de março de 2021): 2150065. http://dx.doi.org/10.1142/s0217751x21500652.

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The effect of the geometry (deviation from the flat space) on the quantum evolution of the momentum and position of a free particle is discussed. It is shown that beginning with a wave-packet of minimum uncertainty (a Gaussian wave), there is a usual increase in the product of the volume uncertainties in the momentum and position space, as seen in the quantum mechanics on a flat spaces. But there is also a contribution from geometry. The leading order of this contribution is calculated.

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Bersons, Imants, Rita Veilande e Ojars Balcers. "Reflection and refraction of photons". Physica Scripta 97, n.º 3 (11 de fevereiro de 2022): 035504. http://dx.doi.org/10.1088/1402-4896/ac50c4.

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Abstract Three linear equations are proposed as quantum-mechanical equations for the free propagating photons. The solution of these equations is the vector potential of the electromagnetic field and it is a product of the Gaussian functions for the transverse coordinates and the eigenfunction of the harmonic oscillator for the longitudinal coordinate. This solutions is used to describe the reflection and refraction of photons on the boundary between two dielectrics. The amplitude of the reflected field coincides with the Fresnel formulae for the plane waves, but the amplitude of the refracted field is different. These amplitudes are the probability’s amplitudes of reflection and refraction of photons—like in the quantum mechanics. The photons propagated from the first into the second medium increase (decrease) their transverse size in the plane of incidence, if the refraction index of the second medium is greater (smaller) than in the first medium. The increasing or decreasing grow when increasing the angle of incidence. The difference between the quantum mechanics of the particles with a mass and the photons, as well as the interpretation of the wave function of photons, is discussed.

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Ghanbari, Ahmad, e Raziyeh Birooni. "Thermodynamic properties of GaAs quantum dot confined by asymmetric Gaussian potential". High Temperatures-High Pressures 51, n.º 5 (2022): 367–79. http://dx.doi.org/10.32908/hthp.v51.1251.

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In the present work, we have calculated the thermodynamic properties of an asymmetrical Gaussian potential quantum dot under external electric field. To this end, we have solved the Schr�dinger equation and have obtained the energy levels and wave functions, analytically. According to the obtained eigenvalues, we have calculated the partition function of the system by the Poisson summation formalism. Afterward, we have deduced some thermodynamic properties such as mean energy, entropy, specific heat and free energy under the application of an external electric field using the canonical ensemble approach. These thermodynamic properties for an asymmetrical Gaussian potential GaAs quantum dot have been discussed in detail.

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KHRENNIKOV, ANDREI, MASANORI OHYA e NOBORU WATANABE. "QUANTUM PROBABILITY FROM CLASSICAL SIGNAL THEORY". International Journal of Quantum Information 09, supp01 (janeiro de 2011): 281–92. http://dx.doi.org/10.1142/s0219749911007289.

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We present quantum mechanics (QM) as theory of special classical random signals. On one hand, this approach provides a possibility to go beyond conventional QM: to create a finer description of micro processes than given by the QM-formalism. In fact, we present a model with hidden variables of the wave-type. On the other hand, our approach establishes coupling between quantum and classical information theories. We recall that quantum information theory has already been used for description of the entropy of Gaussian input signals for noisy channels. The entropy of a classical random input was invented as the entropy of the quantum density operator corresponding to the covariance operator of the input process.1 In this paper, we proceed the other way around: we apply classical signal theory to create a measurement model which reproduces quantum probabilities.

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Mathai, Arak M. "An Extended Zeta Function with Applications in Model Building and Bayesian Analysis". Mathematics 11, n.º 19 (26 de setembro de 2023): 4076. http://dx.doi.org/10.3390/math11194076.

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In certain problems in model building and Bayesian analysis, the results end up in forms connected with generalized zeta functions. This necessitates the introduction of an extended form of the generalized zeta function. Such an extended form of the zeta function is introduced in this paper. In model building situations and in various types of applications in physical, biological and social sciences and engineering, a basic model taken is the Gaussian model in the univariate, multivariate and matrix-variate situations. A real scalar variable logistic model behaves like a Gaussian model but with a thicker tail. Hence, for many of industrial applications, a logistic model is preferred to a Gaussian model. When we study the properties of a logistic model in the multivariate and matrix-variate cases, in the real and complex domains, invariably the problem ends up in the extended zeta function defined in this paper. Several such extended logistic models are considered. It is also found that certain Bayesian considerations also end up in the extended zeta function introduced in this paper. Several such Bayesian models in the multivariate and matrix-variate cases in the real and complex domains are discussed. It is stated in a recent paper that “Quantum Mechanics is just the Bayesian theory generalized to the complex Hilbert space”. Hence, the models developed in this paper are expected to have applications in quantum mechanics, communication theory, physics, statistics and related areas.

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46

Katz, Daniel. "A new quantum operator for distance". International Journal of Modern Physics A 34, n.º 06n07 (10 de março de 2019): 1950033. http://dx.doi.org/10.1142/s0217751x19500337.

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We introduce a new semirelativistic quantum operator for the length of the worldline a particle traces out as it moves. In this article the operator is constructed in a heuristic way and some of its elementary properties are explored. The operator ends up depending in a very complicated way on the potential of the system it is to act on so as a proof of concept we use it to analyze the expected distance traveled by a free Gaussian wave packet with some initial momentum. It is shown in this case that the distance such a particle travels becomes light-like as its mass vanishes and agrees with the classical result for macroscopic masses. This preliminary result has minor implications for the Weak Equivalence Principle (WEP) in quantum mechanics. In particular it shows that the logical relationship between two formulations of the WEP in classical mechanics extends to quantum mechanics. That our result is qualitatively consistent with the work of others emboldens us to start the task of evaluating the new operator in nonzero potentials. However, we readily acknowledge that the looseness in the definition of our operator means that all of our so-called results are highly speculative. Plans for future work with the new operator are discussed in the last section.

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Hsu, Li-Yi, Shoichi Kawamoto e Wen-Yu Wen. "Entropic uncertainty relation based on generalized uncertainty principle". Modern Physics Letters A 32, n.º 28 (4 de setembro de 2017): 1750145. http://dx.doi.org/10.1142/s0217732317501450.

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We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so-called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.

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DEKKER, H. "EFFECTIVE DIPOLE-RADIATION-FIELD THEORY II: ALL ORDERS BEYOND STANDARD COUPLING". International Journal of Modern Physics B 10, n.º 10 (30 de abril de 1996): 1211–25. http://dx.doi.org/10.1142/s0217979296000453.

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The novel treatment of the interaction between a charged particle and the electromagnetic field, as presented in paper I [H. Dekker, Int. J. Mod. Phys.B8, 1–19 (1994)], is generalized to all orders beyond the standard dipole model. The resulting nonlinear problem is then again statistically linearized and the ensuing dynamics is solved exactly for a harmonically bound nonrelativistic electron. The earlier noted ultraviolet divergence in the system’s quantum mechanics is found to be absent, unless the bare electron mass were exactly zero. Inter alia it is also found that the electron’s generic quantum distribution is Gaussian.

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Alvarez-Estrada, Ramón F. "Models of macromolecular chains based on Classical and Quantum Mechanics: comparison with Gaussian models". Macromolecular Theory and Simulations 9, n.º 2 (1 de fevereiro de 2000): 83–114. http://dx.doi.org/10.1002/(sici)1521-3919(20000201)9:2<83::aid-mats83>3.0.co;2-x.

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Lasser, Caroline, e Chunmei Su. "Various variational approximations of quantum dynamics". Journal of Mathematical Physics 63, n.º 7 (1 de julho de 2022): 072107. http://dx.doi.org/10.1063/5.0088265.

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We investigate variational principles for the approximation of quantum dynamics that apply for approximation manifolds that do not have complex linear tangent spaces. The first one, dating back to McLachlan [Mol. Phys. 8, 39–44 (1964)], minimizes the residuum of the time-dependent Schrödinger equation, while the second one, originating from the lecture notes of Kramer and Saraceno [ Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics Vol. 140 (Springer, Berlin, 1981)], imposes the stationarity of an action functional. We characterize both principles in terms of metric and symplectic orthogonality conditions, consider their conservation properties, and derive an elementary a posteriori error estimate. As an application, we revisit the time-dependent Hartree approximation and frozen Gaussian wave packets.

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