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Academic literature on the topic 'Quantum trajectorie'

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Published: 9 March 2023
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Journal articles on the topic "Quantum trajectorie"

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Yang, Ciann-Dong, and Shiang-Yi Han. "Tunneling Quantum Dynamics in Ammonia." International Journal of Molecular Sciences 22, no. 15 (July 31, 2021): 8282. http://dx.doi.org/10.3390/ijms22158282.

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Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem; there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.
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CARIÑO, RICOLINDO L., IOANA BANICESCU, RAVI K. VADAPALLI, CHARLES A. WEATHERFORD, and JIANPING ZHU. "PARALLEL ADAPTIVE QUANTUM TRAJECTORY METHOD FOR WAVEPACKET SIMULATIONS." Parallel Processing Letters 15, no. 04 (December 2005): 415–22. http://dx.doi.org/10.1142/s0129626405002337.

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Time-dependent wavepackets are widely used to model various phenomena in physics. One approach in simulating the wavepacket dynamics is the quantum trajectory method (QTM). Based on the hydrodynamic formulation of quantum mechanics, the QTM represents the wavepacket by an unstructured set of pseudoparticles whose trajectories are coupled by the quantum potential. The governing equations for the pseudoparticle trajectories are solved using a computationally-intensive moving weighted least squares (MWLS) algorithm, and the trajectories can be computed in parallel. This paper contributes a strategy for improving the performance of wavepacket simulations using the QTM. Specifically, adaptivity is incorporated into the MWLS algorithm, and loop scheduling techniques are employed to dynamically load balance the parallel computation of the trajectories. The adaptive MWLS algorithm reduces the amount of computations without sacrificing accuracy, while adaptive loop scheduling addresses the load imbalance introduced by the algorithm and the runtime system. Results of experiments on a Linux cluster are presented to confirm that the adaptive MWLS reduces the trajectory computation time by up to 24%, and adaptive loop scheduling achieves parallel efficiencies of up to 85% when simulating a free particle.
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NADAI, Kamila Nogueira Gabriel De, and Adriano Pereir JARDIM. "Gestalt-terapia e física quântica: um diálogo possível." PHENOMENOLOGICAL STUDIES - Revista da Abordagem Gestáltica 16, no. 2 (2010): 157–66. http://dx.doi.org/10.18065/rag.2010v16n2.4.

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This study offers an epistemological discussion about the classic psychology and one of its present components, Gestalt therapy, using the trajectory of classical physics to quantum as a backdrop. There was a discussion through a review by addressing three points involving dichotomous (and still currently involved) a partial transition from classical physics to quantum physics (linearity versus nonlinearity; action and reaction versus complex; and classical mechanics versus quantum mechanics) and, illustratively, three points of discussion related to classical psychology as opposed to Gestalt therapy (causal versus existentialism; elementarism versus holism, and objectivity versus phenomenology). It was concluded that there are differences and similarities in the trajectories analyzed, as the paradoxical properties of its objects, the quantum and human consciousness, setting up contact points that enable a dialogue between both quantum physics and Gestalt-therapy.
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Hiley, Basil, and Peter Van Reeth. "Quantum Trajectories: Real or Surreal?" Entropy 20, no. 5 (May 8, 2018): 353. http://dx.doi.org/10.3390/e20050353.

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The claim of Kocsis et al. to have experimentally determined “photon trajectories” calls for a re-examination of the meaning of “quantum trajectories”. We will review the arguments that have been assumed to have established that a trajectory has no meaning in the context of quantum mechanics. We show that the conclusion that the Bohm trajectories should be called “surreal” because they are at “variance with the actual observed track” of a particle is wrong as it is based on a false argument. We also present the results of a numerical investigation of a double Stern-Gerlach experiment which shows clearly the role of the spin within the Bohm formalism and discuss situations where the appearance of the quantum potential is open to direct experimental exploration.
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HUANG, JUNG-JENG. "PILOT-WAVE SCALAR FIELD THEORY IN DE SITTER SPACE: LATTICE SCHRÖDINGER PICTURE." Modern Physics Letters A 25, no. 01 (January 10, 2010): 1–13. http://dx.doi.org/10.1142/s0217732310032263.

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In the lattice Schrödinger picture, we find the de Broglie–Bohm quantum trajectories for the eigenstates of a generically coupled free real scalar field in de Sitter space. For the massless minimally coupled scalar field which has exact quantum trajectory, we evaluate both the time evolution of vacuum state and the possible effects of initial quantum nonequilibrium on the power spectrum of the primordial inflaton and curvature fluctuations in the slow-roll approximation. We reproduce the results that were already presented by Valentini who considered only the massless minimal coupling case. In addition we cover both massive minimal and massive non-minimal coupling cases which are the extension of Valentini's work. Finally we discuss the difference between de Broglie's first-order dynamics and Bohm's second-order dynamics in finding the quantum trajectories.
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SHOJAI, ALI, and FATIMAH SHOJAI. "CAUSAL LOOP QUANTUM COSMOLOGY IN MOMENTUM SPACE." International Journal of Modern Physics D 18, no. 01 (January 2009): 83–93. http://dx.doi.org/10.1142/s0218271809014339.

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We shall show that it is possible to make a causal interpretation of loop quantum cosmology using the momentum as the dynamical variable. We shall show that one can derive Bohmian trajectories. For a sample cosmological solution with cosmological constant, the trajectory is plotted.
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Błaszak, Maciej, and Ziemowit Domański. "Quantum trajectories." Physics Letters A 376, no. 47-48 (November 2012): 3593–98. http://dx.doi.org/10.1016/j.physleta.2012.10.030.

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Dorsselaer, F. E. van, and G. Nienhuis. "Quantum trajectories." Journal of Optics B: Quantum and Semiclassical Optics 2, no. 4 (June 21, 2000): R25—R33. http://dx.doi.org/10.1088/1464-4266/2/4/201.

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Szanyi, I., and V. Svintozelskyi. "Pomeron-Pomeron Scattering." Ukrainian Journal of Physics 64, no. 8 (September 18, 2019): 760. http://dx.doi.org/10.15407/ujpe64.8.760.

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The central exclusive diffractive (CED) production of meson resonances potentially is a factory producing new particles, in particular, a glueball. The produced resonances lie on trajectories with vacuum quantum numbers, essentially on the pomeron trajectory. A tower of resonance recurrences, the production cross-section, and the resonances widths are predicted. A new feature is the form of a non-linear pomeron trajectory, producing resonances (glueballs) with increasing widths. At LHC energies, in the nearly forward direction, the t-channel both in elastic, single, or double diffraction dissociations, as well as in CED, is dominated by the pomeron exchange (the role of secondary trajectories is negligible, however a small contribution from the odderon may be present).
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Goan, H.-S. "An analysis of reading out the state of a charge quantum bit." Quantum Information and Computation 3, no. 2 (March 2003): 121–38. http://dx.doi.org/10.26421/qic3.2-4.

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We provide a unified picture for the master equation approach and the quantum trajectory approach to a measurement problem of a two-state quantum system (a qubit), an electron coherently tunneling between two coupled quantum dots (CQD's) measured by a low transparency point contact (PC) detector. We show that the master equation of ``partially'' reduced density matrix can be derived from the quantum trajectory equation (stochastic master equation) by simply taking a ``partial'' average over the all possible outcomes of the measurement. If a full ensemble average is taken, the traditional (unconditional) master equation of reduced density matrix is then obtained. This unified picture, in terms of averaging over (tracing out) different amount of detection records (detector states), for these seemingly different approaches reported in the literature is particularly easy to understand using our formalism. To further demonstrate this connection, we analyze an important ensemble quantity for an initial qubit state readout experiment, P(N,t), the probability distribution of finding N electron that have tunneled through the PC barrier(s) in time t. The simulation results of P(N,t) using 10000 quantum trajectories and corresponding measurement records are, as expected, in very good agreement with those obtained from the Fourier analysis of the ``partially'' reduced density matrix. However, the quantum trajectory approach provides more information and more physical insights into the ensemble and time averaged quantity P(N,t). Each quantum trajectory resembles a single history of the qubit state in a single run of the continuous measurement experiment. We finally discuss, in this approach, the possibility of reading out the state of the qubit system in a single-shot experiment.
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Dissertations / Theses on the topic "Quantum trajectorie"

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ALBARELLI, FRANCESCO. "CONTINUOUS MEASUREMENTS AND NONCLASSICALITY AS RESOURCES FOR QUANTUM TECHNOLOGIES." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/602166.

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This PhD thesis contains results about two different main topics. The first part deals with the application of continuously monitored quantum systems to high precision quantum metrology. A continuous in time measurement on a quantum system is a kind indirect measurement, which only weakly perturbs the system and leaves room for it to evolve under its dynamics. This time-continuous measurement allows one to collect information about some interesting parameter characterizing the dynamics. In this thesis we show how to apply the theory of quantum parameter estimation to continuously monitored quantum systems. In particular, we study the estimation of a magnetic field applied to an ensemble of two level atoms; we show that by continuously monitoring the system we can obtain a quadratic scaling of the precision with the number of atoms, in two different physical settings (dynamically generated entanglement or initial entanglement). In the second part we study different aspects of nonclassicality of continuous variable quantum systems (bosonic degree of freedoms). They can be described by distributions (in particular, the Wigner function) on a classical phase space, which however can take negative values, the hallmark of nonclassicality. In this context, states with a Gaussian distribution are very useful and very well studied; however, on a fundamental level they must be considered classical. We present several studies connected to the vast topic of non-Gaussian states, starting from an application to parameter estimation, as a link to the first part. We study the relationships between anharmonic Hamiltonians and the nonclassicality of their ground states; we also explore the connection between a quantum effect called `backflow of probability' and the negativity of the Wigner function. We end by showing that quantum operations made out of Gaussian building blocks give rise to a well-defined resource theory of Wigner negativity and non-Gaussianity.
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Campagne-Ibarcq, Philippe. "Quantum backaction and feedback in superconducting circuits." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0011/document.

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Cette thèse décrit une série d’expériences mettant en lumière l’action en retour de la mesure et la décohérence pour un système quantique ouvert élémentaire, le qubit supraconducteur. Ces observations sont rendues possibles grâce au développement récent d’amplificateurs Josephson proches de la limite quantique. L’information extraite du système peut être utilisée dans des boucles de rétroaction quantique. Pour stabiliser un état arbitraire prédéterminé du qubit, une mesure projective est réalisée périodiquement et une boucle de rétroaction permet de corriger les erreurs détectées. En se substituant à l'environnement et en réalisant une mesure hétérodyne continue de la fluorescence du qubit, nous reconstituons des trajectoires quantiques individuelles lors de sa relaxation. En conditionnant cette détection au résultat d'une mesure projective postérieure, nous déterminons les weak values du signal de fluorescence. En formant une boucle de rétroaction continue à partir de ce signal, nous stabilisons également un état arbitraire du qubit. Enfin, nous observons dans une dernière expérience la dynamique quantique Zénon d'un mode micro-onde, induite par son couplage au qubit
This thesis presents a series of experiments highlighting measurement back action and decoherence in a basic open quantum system, the superconducting qubit. These observations are enabled by recent advances in amplification close to the quantum limit using Josephson circuits. The information extracted from the system can then be used as input in quantum feedback. A stroboscopic projective readout is performed and a feedback loop is used to correct for detected errors, thus stabilizing an arbitrary predetermined state of the qubit. When monitoring continuously the environment of the qubit by heterodyne detection of its fluorescence, we reconstruct individual quantum trajectories during relaxation. Conditioning this detection to the outcome of a following projective measurement, we access the weak values of the fluorescence signal. Included in a continuous feedback loop, this detection is also used to stabilize an arbitrary state of the qubit. Finally, a last experiment witnesses quantum Zeno dynamics of a resonant microwave mode, entailed by its coupling to the qubit
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Benoist, Tristan. "Open quantum systems and quantum stochastic processes." Thesis, Paris, Ecole normale supérieure, 2014. http://www.theses.fr/2014ENSU0006/document.

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De nombreux phénomènes de physique quantique ne peuvent être compris que par l'analyse des systèmes ouverts. Un appareil de mesure, par exemple, est un système macroscopique en contact avec un système quantique. Ainsi, tout modèle d'expérience doit prendre en compte les dynamiques propres aux systèmes ouverts. Ces dynamiques peuvent être complexes : l'interaction du système avec son environnement peut modifier ses propriétés, l'interaction peu créer des effets de mémoire dans l'évolution du système, . . . Ces dynamiques sont particulièrement importantes dans l'étude des expériences d'optique quantique. Nous sommes aujourd'hui capables de manipuler individuellement des particules. Pour cela la compréhension et le contrôle de l'influence de l'environnement est crucial. Dans cette thèse nous étudions d'un point de vue théorique quelques procédures communément utilisées en optique quantique. Avant la présentation de nos résultats, nous introduisons et motivons l'utilisation de la description markovienne des systèmes quantiques ouverts. Nous présentons a la fois les équations maîtresses et le calcul stochastique quantique. Nous introduisons ensuite la notion de trajectoire quantique pour la description des mesures indirectes continues. C'est dans ce contexte que l'on présente les résultats obtenus au cours de cette thèse. Dans un premier temps, nous étudions la convergence des mesures non destructives. Nous montrons qu'elles reproduisent la réduction du paquet d'onde du système mesuré. Nous montrons que cette convergence est exponentielle avec un taux fixe. Nous bornons le temps moyen de convergence. Dans ce cadre, en utilisant les techniques de changement de mesure par martingale, nous obtenons la limite continue des trajectoires quantiques discrètes. Dans un second temps, nous étudions l'influence de l'enregistrement des résultats de mesure sur la préparation d'état par ingénierie de réservoir. Nous montrons que l'enregistrement des résultats de mesure n'a pas d'influence sur la convergence proprement dite. Cependant, nous trouvons que l'enregistrement des résultats de mesure modifie le comportement du système avant la convergence. Nous retrouvons une convergence exponentielle avec un taux équivalent au taux sans enregistrement. Mais nous trouvons aussi un nouveau taux de convergence correspondant a une stabilité asymptotique. Ce dernier taux est interprété comme une mesure non destructive ajoutée. Ainsi l'état du système ne converge qu'après un temps aléatoire. A partir de ce temps la convergence peut être bien plus rapide. Nous obtenons aussi une borne sur le temps moyen de convergence
Many quantum physics phenomena can only be understood in the context of open system analysis. For example a measurement apparatus is a macroscopic system in contact with a quantum system. Therefore any experiment model needs to take into account open system behaviors. These behaviors can be complex: the interaction of the system with its environment might modify its properties, the interaction may induce memory effects in the system evolution, ... These dynamics are particularly important when studying quantum optic experiments. We are now able to manipulate individual particles. Understanding and controlling the environment influence is therefore crucial. In this thesis we investigate at a theoretical level some commonly used quantum optic procedures. Before the presentation of our results, we introduce and motivate the Markovian approach to open quantum systems. We present both the usual master equation and quantum stochastic calculus. We then introduce the notion of quantum trajectory for the description of continuous indirect measurements. It is in this context that we present the results obtained during this thesis. First, we study the convergence of non demolition measurements. We show that they reproduce the system wave function collapse. We show that this convergence is exponential with a fixed rate. We bound the mean convergence time. In this context, we obtain the continuous time limit of discrete quantum trajectories using martingale change of measure techniques. Second, we investigate the influence of measurement outcome recording on state preparation using reservoir engineering techniques. We show that measurement outcome recording does not influence the convergence itself. Nevertheless, we find that measurement outcome recording modifies the system behavior before the convergence. We recover an exponential convergence with a rate equivalent to the rate without measurement outcome recording. But we also find a new convergence rate corresponding to an asymptotic stability. This last rate is interpreted as an added non demolition measurement. Hence, the system state converges only after a random time. At this time the convergence can be much faster. We also find a bound on the mean convergence time
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Weber, Steven Joseph. "Quantum Trajectories of a Superconducting Qubit." Thesis, University of California, Berkeley, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3686046.

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In quantum mechanics, the process of measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. An accurate measurement record documents this stochastic evolution and can be used to reconstruct the quantum trajectory of the system state in a single experimental iteration. We use weak measurements to track the individual quantum trajectories of a superconducting qubit that evolves under the competing influences of continuous weak measurement and Rabi drive. We analyze large ensembles of such trajectories to examine their characteristics and determine their statistical properties. For example, by considering only the subset of trajectories that evolve between any chosen initial and final states, we can deduce the most probable path through quantum state space. Our investigation reveals the rich interplay between measurement dynamics, typically associated with wavefunction collapse, and unitary evolution. Our results provide insight into the dynamics of open quantum systems and may enable new methods of quantum state tomography, quantum state steering through measurement, and active quantum control.

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Warszawski, Prahlad. "Quantum Trajectories For, and As, Understanding." Thesis, University of Sydney, 2020. https://hdl.handle.net/2123/24237.

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Quantum trajectories provide a fundamental description of the measurement of individual quantum systems. As such, they have wide impact, and application, in the emerging field of quantum technology. Importantly, they also give a mechanism for developing our understanding of the nature of quantum mechanics. In Part I of this thesis, we develop and apply quantum trajectory methods, with a focus upon experimentally relevant optomechanical systems. By solving the stochastic master equation for sufficiently simple bosonic systems, and subsequently finding the positive operator-valued measure (POVM), we are able to conduct a detailed study of the use of parametric amplification for quantum state tomography of nonclassical optomechanical states of motion. Homodyne tomography is a cornerstone experimental tool, and an analysis of its convergence is carried out in the presence of realistic imperfections. We complete Part I by conducting a detailed preparatory analysis of superfluid optomechanical systems possessing vorticity. Part II of this thesis investigates the correspondence between open classical and open quantum systems. We prove a result shows that open quantum systems are, in general, harder to track than open classical systems. We couch this result in terms of physically realisable ensembles (PREs), which can describe the dynamics of a monitored, $D$-dimensional, quantum system obeying a master equation that has reached equilibrium. Associated with the PRE is a measurement scheme that leads to quantum trajectories in which the system evolution consists purely of jumps between the states that are members of the PRE. The occupation of the $K$, generally non-orthogonal, states in the ensemble can be used to track the system. The number of states in the ensemble, $K$, represents the amount of memory that is required to do so. In comparison, a classical $D$-dimensional system requires occupation of the $D$ states to be tracked. After first developing analysis tools that make feasible the discovery of PREs in $D>2$, we prove our main result that there are quantum systems that have a minimal sized PRE with $K>D$.
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Avanzini, Francesco. "Quantum molecular trajectory and stochastic theories of quantum fluctuations." Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3424724.

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Bohm theory is a formulation of Quantum Mechanics that characterises the state of a quantum system according to both the wave function, as in the conventional formulation, and the coordinates (positions) of all the particles that evolve in time drawing quantum continuous trajectories. Furthermore, a statistical ensemble of all the possible trajectories, raising from the impossibility to know the initial position of all the particles, establishes the exact correspondence with the traditional Quantum Mechanics. From a computational point of view, Bohm theory has found many applications in Chemical Physics especially to develop new methodologies for solving the Schrödinger equation and to address semi-classical approximations of Quantum Mechanics. From a theoretical point of view, the most appealing feature of Bohm theory is its capability to supply a conceptual map between the quantum formalism and our representation of what a chemical system is. Chemical systems are composed of molecules, but the same idea of molecule requires a specific arrangement in the space of particles, i.e., the nuclei of the atoms. The statistical description of conventional Quantum Mechanics on the basis of wave function alone is insufficient to establish a clear correspondence with such a picture of molecules. Indeed, chemists employ usually Classical Mechanics in order to overcome this drawback of the standard quantum theory. On the other hand, if the particles position is included in the quantum formalism, as Bohm theory does, the map can be defined in a self-consistent way. In other words, Bohm theory appears to be the suitable quantum framework to represent molecules and their motion. The chemical representation of molecular systems finds a natural correspondence with a single Bohm trajectory, since it is always implicitly assumed that molecular components have specific spatial position independently of our knowledge about it. Consequently, we develop a quantum method whose fundamental assumption is that a single Bohm trajectory, i.e., a quantum molecular trajectory, describes the molecular systems and the molecular motion correctly.
First of all, we examine the correspondence between a single Bohm trajectory and the conventional Quantum Mechanics, without using the ensemble of trajectories. We verify that such a correspondence exists through numerical simulations and we prove formally that the statistical properties of a single Bohm trajectory explain the probabilistic description of Quantum Mechanics. Once the consistency of this original approach has been established, we investigate the predicted properties. For instance, we take into account the constants of motion (such as the energy) corresponding to the time evolution of the coordinates and the behaviour of simple chemical systems, e.g., the vibrational motion of single molecules interacting with a resonant field. In this way, unexpected features of the molecular motion are found. Secondly, we tackle the challenge of describing many components systems (like the chemical systems in ordinary conditions). As a matter of fact, the computation of the Bohm trajectory and of the wave function is extremely demanding. However, the statistical properties of the Bohm trajectory allow the derivation of stochastic theories for examining the dynamics of open quantum systems, i.e., few molecules (or few degrees of freedom) interacting with their environment (the other molecules). One of the developed stochastic methods correlates the dynamics of the reduced density matrix, for the degrees of freedom of interest, to the evolution of the corresponding Bohm coordinates. In other words, the Bohm equation, determining the set of all the particles velocities according to the full wave function, is replaced with a stochastic one that approximates the velocity of a subset of coordinates according to the reduced density matrix. In such a way, the quantum fluctuations induced by the environment are taken into account. The advantage of this method concerns its capability of describing quantum systems, including open quantum systems, in terms of a quantum trajectory. This could allow the understanding of the molecular motion during a spectroscopical experiment. The possibility of investigating reactive systems, such as conformational changes, is particularly interesting. As a matter of fact, chemical reactions can be completely characterised only through the particles motion and we define the suit- able quantum methodology providing a self-consistent description of the molecular motion.
La teoria di Bohm è una formulazione della Meccanica Quantistica che caratterizza lo stato di un sistema quantistico attraverso sia la funzione d’onda, come la teoria standard, sia le coordinate (le posizioni) di tutte le particelle che evolvono nel tempo secondo traiettorie quantistiche continue. Inoltre, un ensemble statistico di tutte le possibile traiettorie, che deriva dall’impossibilità di conoscere la posizione iniziale di tutte le particelle, stabilisce l’esatta corrispondenza con la Meccanica Quantistica tradizionale. Da un punto di vista computazionale, la teoria di Bohm è stata impiegata in Chimica Fisica principalmente per sviluppare nuove strategie risolutive dell’equazione di Schrödinger o nuove approssimazioni semi-classiche della Meccanica Quantistica. Da un punto di vista teorico, la caratteristica più attraente della teoria di Bohm è quella di essere il contesto naturale per definire un mappa concettuale tra il formalismo quantistico e la nostra rappresentazione dei sistemi chimici. I sistemi chimici sono composti di molecole, ma l’idea stessa di molecola è associata ad una specifica posizione spaziale delle particelle, i.e., i nuclei degli atomi. La descrizione statistica della Meccanica Quantistica convenzionale, sulla base della sola funzione d’onda, è insufficiente per definire una chiara corrispondenza con questa immagine delle molecole. Infatti, i chimici fanno spesso affidamento alla Meccanica Classica per aggirare questa difficoltà della teoria quantistica standard. Tuttavia, se la posizione delle particelle è inclusa nel formalismo quantistico, così come fa la teoria di Bohm, la corrispondenza può essere definita in modo autoconsistente. In altre parole, la teoria di Bohm sembra essere il contesto formale idoneo per rappresentare quantisticamente le molecole e il loro moto. Comunque, la raffigurazione chimica dei sistemi molecolari corrisponde ad una singola traiettoria di Bohm dato che si assume implicitamente che i componenti delle molecole abbiano una specifica posizione spaziale indipendentemente dal fatto che essa sia nota o meno. Di conseguenza, si è sviluppata una metodologia quantistica che si basa sull’assunzione che una singola traiettoria di Bohm, cioè una traiettoria molecolare quantistica, descrive correttamente i sistemi molecolari e il moto molecolare. In primo luogo, viene esaminata la corrispondenza tra una singola traiettoria di Bohm e la Meccanica Quantistica convenzionale dato che si rinuncia all’ensemble di traiettorie. Si verifica che tale corrispondenza esiste attraverso un esperimento numerico e si dimostra formalmente che le proprietà statistiche di una singola traiettoria spiegano la descrizione probabilistica della Meccanica Quantistica. Una volta che la coerenza di questa metodologia è stata verificata, vengono esaminate accuratamente le sue previsioni. Per esempio, si prendono in considerazione le costanti del moto (come l’energia) associate all’evoluzione temporale delle particelle e il comportamento di semplici sistemi chimici, e.g., il moto vibrazionale di singole molecole che interagiscono con un campo esterno risonante. In questo modo, proprietà inaspettate del moto molecolare emergono naturalmente. In secondo luogo, si considera la sfida di descrivere sistemi a molti componenti (quali sono i sistemi chimici in condizioni ordinarie). È ben noto che il calcolo della traiettoria di Bohm e della funzione d’onda è molto costoso computazionalmente. Comunque, le proprietà statistiche della traiettoria di Bohm permettono di derivare teorie stocastiche per esaminare la dinamica di sistemi quantistici aperti, come qualche molecola (o qualche grado di libertà) interagente con l’ambiente (le altre molecole). Uno dei metodi stocastici sviluppati correla la dinamica della matrice densità ridotta, per i gradi di libertà di interesse, all’evoluzione delle corrispondenti coordinate di Bohm. In altre parole, l’equazione di Bohm, che determina la velocità delle particelle attraverso la funzione d’onda, è sostituita da un’equazione stocastica che approssima la velocità di un sott’insieme di coordinate attraverso la matrice densità ridotta. In questo modo, le fluttuazioni quantistiche indotte dall’ambiente sono prese in considerazione. Il vantaggio del metodo riguarda la sua capacità di descrivere i sistemi quantistici, compresi quelli aperti, in termini di una traiettoria quantistica. Questo potrebbe permettere la comprensione del moto molecolare durante un esperimento spettroscopico. Di particolare interesse è la possibilità di esaminare sistemi reattivi, come quelli in cui avvengono cambi conformazionali. Come è ben noto, le reazioni chimiche possono essere totalmente caratterizzate solo attraverso il moto delle particelle e in questa tesi viene definita esattamente una metodologia quantistica che fornisce una descrizione autoconsistente del moto molecolare.
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Buercklin, Samuel Adam. "Optimal trajectories for fast quantum harmonic transport." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/121733.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 85-88).
The transport of atomic ions trapped within a harmonic potential arises necessarily in the course of building a trapped ion quantum computer. We may define this problem in terms of a differential equation and its corresponding boundary conditions to satisfy which are sufficient to guarantee the motional quantum state of the ion is unaltered. However, the solution space to this problem is uncountably large, and the various solutions differ in many qualitative and quantitative aspects. We present an easily-computed functional of transport trajectories with intuitively interpretable terms which may be used to compare solutions to the quantum harmonic transport problem, but does not require an expensive quantum-mechanical simulation of the ion dynamics. Furthermore, we prove the convexity of this cost function under easily satisfied conditions in a Fourier Series parameterization of the problem. We then numerically optimize the cost function to discover optimal trajectories for the quantum harmonic transport problem.
by Samuel Adam Buercklin.
S.M.
S.M. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science
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Koch, Werner. "Non-Markovian Dissipative Quantum Mechanics with Stochastic Trajectories." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-63671.

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All fields of physics - be it nuclear, atomic and molecular, solid state, or optical - offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called "the environment" may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach. With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces. The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems. As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time propagation - until thermalization is reached - is shown to be possible with the presented approach. The properties of the thermalized density are determined and they are ascertained to be independent of the system's initial state. Furthermore, the dependence on the bath's temperature and coupling strength is analyzed and it is demonstrated how a change of the bath parameters can be used to tune the system from the dissociative to the bound regime. A second investigation is conducted for a dissipative tunneling scenario in which a wave packet impinges on a barrier. The dependence of the transmission probability on the initial state's kinetic energy as well as the bath's temperature and coupling strength is computed. For both systems, a comparison with the high-temperature Markovian quantum Brownian limit is performed. The importance of a full non-Markovian treatment is demonstrated as deviations are shown to exist between the two descriptions both in the low temperature cases where they are expected and in some of the high temperature cases where their appearance might not be anticipated as easily.
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Kuipers, Jack Anton. "Correlated Trajectories in Semiclassical Approaches to Quantum Chaos." Thesis, University of Bristol, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486392.

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This thesis is concerned with the application and extension of semiclassical methods, involving correlated trajectories, that were recently developed to explain the observed universal statistics of classically chaotic quantum systems. First we consider systems that depend on an external parameter that does not change the symmetry of the system. 'Ve study correlations between the spectra at different values of the param~ter, a scaled distance x apart, via the parametric spectral form factor K(r, x). Using a semiclassical periodic orbit expansion, we obtain a small r expansion that agrees with random matrix theory for systems with and without time reversal symmetry. Then we consider correlations of the Wigner time delay in open systems. We study a form factor K (r, x, y, M) that depends on the number of scattering channels M, the non-symmetry breaking parameter difference x and also a symmetry breaking parameter y. TheWigner time delay can be expressed semiclassically in terms of the trapped periodic orbits of the system, and using a periodic orbit expansion we obtain several terms in the small r expansion of the form factor that are identical to those calculated from random matrix theory. The Wigner time delay can also be expressed in terms of scattering trajectories that enter and leave the system. Starting from this picture, we derive all terms in the periodic orbit formula and therefore show how the two pictures of the time delay are related on a semiclassical level. A new type of trajectory correlation is derived which recreates the terms from the trapped periodic orbits. This involves two trajectories approaching the same trapped periodic orbit closely - one trajectory approaches the orbit and follows it for several traversals, while its partner approaches in almost the same way but follows the periodic orbit an additional number of times.
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Sutcliffe, Julia H. "Quantum studies of molecular dynamics." Thesis, University of Nottingham, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282566.

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Books on the topic "Quantum trajectorie"

1

Quantum trajectories. Boca Raton: CRC Press, 2010.

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Barchielli, Alberto, and Matteo Gregoratti. Quantum Trajectories and Measurements in Continuous Time. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01298-3.

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Quantum optics: Including noise reduction, trapped ions, quantum trajectories, and decoherence. 2nd ed. Berlin: Springer, 2008.

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Orszag, Miguel. Quantum optics: Including noise reduction, trapped ions, quantum trajectories, and decoherence. Berlin: Springer, 2000.

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Orszag, Miguel. Quantum Optics: Including Noise Reduction, Trapped Ions, Quantum Trajectories, and Decoherence. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000.

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(Matteo), Gregoratti M., and SpringerLink (Online service), eds. Quantum trajectories and measurements in continuous time: The diffusive case. Berlin: Springer, 2009.

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Sanz, Ángel S., and Salvador Miret-Artés. A Trajectory Description of Quantum Processes. II. Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-17974-7.

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Sanz, Ángel S., and Salvador Miret-Artés. A Trajectory Description of Quantum Processes. I. Fundamentals. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-18092-7.

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Ceresole, A. Tullio Regge: An eclectic genius : from quantum gravity to computer play. Edited by Frè P. editor. Singapore: World Scientific Publishing Co. Pte. Ltd., 2020.

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A, Ranfagni, ed. Trajectories and rays: The path-summation in quantum mechanics and optics. Singapore: World Scientific, 1990.

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Book chapters on the topic "Quantum trajectorie"

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Orszag, Miguel. "Quantum Trajectories." In Quantum Optics, 249–79. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29037-9_16.

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Orszag, Miguel. "Quantum Trajectories." In Quantum Optics, 205–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04114-7_16.

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Milburn, G. J., J. K. Breslin, and H. M. Wiseman. "Quantum Trajectories for Quantum Optical Systems." In Quantum Communications and Measurement, 251–64. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1391-3_24.

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Liniov, Alexey, Valentin Volokitin, Iosif Meyerov, Mikhail Ivanchenko, and Sergey Denisov. "Increasing Performance of the Quantum Trajectory Method by Grouping Trajectories." In Communications in Computer and Information Science, 136–50. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71255-0_11.

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Sanz, Ángel S., and Salvador Miret-Artés. "Quantum Mechanics with Trajectories." In A Trajectory Description of Quantum Processes. I. Fundamentals, 187–230. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-18092-7_6.

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Brun, Todd A. "Decoherence and Quantum Trajectories." In Decoherence and Entropy in Complex Systems, 239–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-40968-7_17.

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Barker, John R. "Trajectories in Quantum Transport." In Quantum Transport in Ultrasmall Devices, 171–80. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-1967-6_7.

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Maassen, Hans, and Burkhard Kümmerer. "Purification of quantum trajectories." In Institute of Mathematical Statistics Lecture Notes - Monograph Series, 252–61. Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006. http://dx.doi.org/10.1214/lnms/1196285826.

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Dürr, Detlef, and Dustin Lazarovici. "Weak Measurements of Trajectories." In Understanding Quantum Mechanics, 149–60. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40068-2_8.

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Hegerfeldt, Gerhard C. "The Quantum Jump Approach and Quantum Trajectories." In Irreversible Quantum Dynamics, 233–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44874-8_13.

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Conference papers on the topic "Quantum trajectorie"

1

Carmichael, H. J., L. Tian, and P. Kochan. "Decay of quantum coherence using quantum trajectories." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.mff4.

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In the quantum trajectory approach an open quantum system is represented by a stochastic pure-state wave function. The mixed-state density operator that satisfies the usual master equation is recovered from the quantum trajectories by performing either an ensemble average or, for stationary systems, an average over time. This unraveling of the master equation dynamics into pure-state trajectories provides new insight into the decay of quantum coherence in systems that are open to the environment. Under some conditions macroscopic superposition states are preserved as macroscopic superposition states along individual trajectories, but are reduced to mixtures by the trajectory average. Under other conditions one of the states in a macroscopic superposition becomes dominant (in amplitude) over the other along each quantum trajectory. We discuss the mechanisms that produce these dynamics and assess the implications for the observation of Schrodinger cat states in optics experiments. We present results for some specific examples of macroscopic superposition states generated by a cavity QED system. The system involves a small collection of atoms in an optical cavity driven by a coherent laser field. Under strong-coupling conditions this system produces a variety of Schrodinger cat states whose precise form depends on the number of atoms, the method of excitation (through a cavity mirror or from the side), the initial state of the atoms, and the position of the atoms in the cavity.
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Yu, Ting. "Approaches to Non-Markovian Quantum Open Systems: From Quantum Trajectories to Master Equations." In Workshop on Entanglement and Quantum Decoherence. Washington, D.C.: Optica Publishing Group, 2008. http://dx.doi.org/10.1364/weqd.2008.nmd3.

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In this tutorial, I will review some recent progresses in non-Markovian dynamics of quantum open systems. I will be focused with non-Markovian quantum trajectories and non-Markovian master equation approaches. In particular, I will show how to derive an exact non-Markovian master equation from the corresponding quantum trajectories. I will also show how to use quantum trajectories to derive the well-known Kraus operators for pure dephasing noise. The applications of quantum trajectories to quantum information and decoherence will be briefly reviewed.
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Dasari, Durga B. Rao, Sen Yang, Jörg Wrachtrup, and Nikolas Abt. "A repository for quantum measurement trajectories." In Quantum Communications and Quantum Imaging XV, edited by Ronald E. Meyers, Yanhua Shih, and Keith S. Deacon. SPIE, 2017. http://dx.doi.org/10.1117/12.2274755.

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Tian, L., and H. J. Carmichael. "Quantum trajectory calculations in cavity QED." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.tujj1.

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We use the quantum trajectory (stochastic wave function) approach to simulate the dynamics of a cavity QED system. The system consists of one atom interacting on resonance with one mode of a coherently driven optical cavity. We simulate a variety of different measurements on this system. The simulation of direct photoelectric detection produces trajectories that illustrate the collapse of the wave function in delayed photon coincidence measurements. It also allows us to calculate waiting-time distributions, pho­toelectron counting distributions, and the mean transmitted intensity as a function of the excitation frequency and field strength. A simulation with frequency filtering of the stochastic wave fuction gives results for optical spectra. From a simulation of homodyne detection we obtain trajectories showing the fluctuations in the quadrature phase amplitudes of the intracavity field and the atomic dipole. These simulations are used to calculate spectra of squeezing. We show that when the cavity is excited near one of the "vacuum" Rabi resonances, the composite atom-cavity system behaves like a two-state system. Under these conditions the optical spectrum shows Mollow sidebands caused by a dynamic Stark shift of the Jaynes-Cummings eigenstates. Thus, in this measurement we are observing the "dressing" of the (one-quantum) dressed states.
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Orszag, Miguel. "Quantum trajectories: physical interpretation." In 3rd Iberoamerican Optics Meeting and 6th Latin American Meeting on Optics, Lasers, and Their Applications, edited by Angela M. Guzman. SPIE, 1999. http://dx.doi.org/10.1117/12.358423.

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Jun, Jin Woo. "Dynamical Localization and Environmental Noise: a Quantum Trajectory." In Workshop on Entanglement and Quantum Decoherence. Washington, D.C.: Optica Publishing Group, 2008. http://dx.doi.org/10.1364/weqd.2008.p3.

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Using the quantum trajectory approach, we study the effects of environmental noise on dynamical localization in a quantum algorithm simulating the kicked rotator. We apply two models that generalize single qubit noisy channels, like phase flip and amplitude damping, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for simulating the quantum kicked rotator in realistic environments.
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BARKER, J. R. "BOHM TRAJECTORIES IN QUANTUM TRANSPORT." In Proceedings of the Conference. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705129_0017.

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SJÖSTRAND, Johannes. "Quantum Resonances and Trapped Trajectories." In Proceedings of the Bologna APTEX International Conference. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812794598_0002.

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Ralph, Jason F., Simon Maskell, Michael Ransom, and Hendrik Ulbricht. "Classical Tracking for Quantum Trajectories." In 2021 IEEE 24th International Conference on Information Fusion (FUSION). IEEE, 2021. http://dx.doi.org/10.23919/fusion49465.2021.9626966.

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Murch, Kater, Mahdi Naghiloo, Dian Tan, Philippe Lewalle, and Andrew Jordan. "Resonance Fluorescence Trajectories of a Superconducting Qubit." In Quantum Information and Measurement. Washington, D.C.: OSA, 2017. http://dx.doi.org/10.1364/qim.2017.qf5a.1.

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Reports on the topic "Quantum trajectorie"

1

Tang, Jau. Classical trajectory versus quantum interference. A linear chain model for the origin of uncertainty broadening. Office of Scientific and Technical Information (OSTI), February 1996. http://dx.doi.org/10.2172/201584.

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Igor D. Kaganovich, Edward A. Startsev, and Ronald C. Davidson. Comparison Of Quantum Mechanical And Classical Trajectory Calculations Of Cross Sections For Ion-Atom Impact Ionization of Negative - And Positive -Ions For Heavy Ion Fusion Applications. Office of Scientific and Technical Information (OSTI), May 2003. http://dx.doi.org/10.2172/814013.

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