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Journal articles on the topic 'Quantum trajectorie'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

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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2

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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3

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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4

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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6

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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7

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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8

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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9

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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10

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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11

Gould, C., A. Sachrajda, Y. Feng, A. Delage, P. Kelly, and P. T. Coleridge. "Demonstration of device conductance modulation by electrostatic control of the electron phase." Canadian Journal of Physics 74, S1 (December 1, 1996): 207–11. http://dx.doi.org/10.1139/p96-860.

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In this paper we describe a novel effect observed in a quantum wire containing two parallel "artificial" (i.e., electrostatically defined antidots) impurities. At low magnetic fields we observe a series of resistance peaks. These occur at magnetic fields for which classical electron trajectories are commensurate with the device geometry. The resistance peaks are modulated by periodic oscillations that can be observed both as a function of the applied magnetic field or the gate voltage, which controls the size of the impurities. These oscillations are analyzed in terms of the classical action of ballistic electrons on closed trajectories, the related phase gained along these trajectories, and the resulting quantum interference effect. We show that these oscillations when observed as a function of gate voltage are consistent with changes of the electron wavelength along part of the electron trajectory. The device conductance is thus being modulated by the electrostatic control of the electron phase.

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12

Gebhart, Valentin, Kyrylo Snizhko, Thomas Wellens, Andreas Buchleitner, Alessandro Romito, and Yuval Gefen. "Topological transition in measurement-induced geometric phases." Proceedings of the National Academy of Sciences 117, no. 11 (March 2, 2020): 5706–13. http://dx.doi.org/10.1073/pnas.1911620117.

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The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous and also underline the physics of robust topological phenomena such as the quantum Hall effect. Equivalently, a geometric phase may be induced through a cyclic sequence of quantum measurements. We show that the application of a sequence of weak measurements renders the closed trajectories, hence the geometric phase, stochastic. We study the concomitant probability distribution and show that, when varying the measurement strength, the mapping between the measurement sequence and the geometric phase undergoes a topological transition. Our finding may impact measurement-induced control and manipulation of quantum states—a promising approach to quantum information processing. It also has repercussions on understanding the foundations of quantum measurement.

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13

Yang, Ciann-Dong, and Shiang-Yi Han. "Extending Quantum Probability from Real Axis to Complex Plane." Entropy 23, no. 2 (February 8, 2021): 210. http://dx.doi.org/10.3390/e23020210.

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Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle’s random motion in the complex plane. The probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution ρc(t,x,y) is verified by the solution of the complex Fokker–Planck equation. It is shown that quantum probability |Ψ|2 and classical probability can be integrated under the framework of complex probability ρc(t,x,y), such that they can both be derived from ρc(t,x,y) by different statistical ways of collecting spatial points.

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14

Holland, Peter. "Trajectory construction of Dirac evolution." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2236 (April 2020): 20190682. http://dx.doi.org/10.1098/rspa.2019.0682.

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We extend our programme of representing the quantum state through exact stand-alone trajectory models to the Dirac equation. We show that the free Dirac equation in the angular coordinate representation is a continuity equation for which the real and imaginary parts of the wave function, angular versions of Majorana spinors, define conserved densities. We hence deduce an exact formula for the propagation of the Dirac spinor derived from the self-contained first-order dynamics of two sets of trajectories in 3-space together with a mass-dependent evolution operator. The Lorentz covariance of the trajectory equations is established by invoking the ‘relativity of the trajectory label'. We show how these results extend to the inclusion of external potentials. We further show that the angular version of Dirac's equation implies continuity equations for currents with non-negative densities, for which the Dirac current defines the mean flow. This provides an alternative trajectory construction of free evolution. Finally, we examine the polar representation of the Dirac equation, which also implies a non-negative conserved density but does not map into a stand-alone trajectory theory. It reveals how the quantum potential is tacit in the Dirac equation.

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15

Dorsselaer, F. E. van, and G. Nienhuis. "Quantum trajectories generalized." Journal of Optics B: Quantum and Semiclassical Optics 2, no. 3 (May 11, 2000): L5—L9. http://dx.doi.org/10.1088/1464-4266/2/3/101.

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16

Villaseco Arribas, Evaristo, Federica Agostini, and Neepa T. Maitra. "Exact Factorization Adventures: A Promising Approach for Non-Bound States." Molecules 27, no. 13 (June 22, 2022): 4002. http://dx.doi.org/10.3390/molecules27134002.

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Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.

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17

Vacchini, Bassano. "General structure of quantum collisional models." International Journal of Quantum Information 12, no. 02 (March 2014): 1461011. http://dx.doi.org/10.1142/s0219749914610115.

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We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time dependent completely positive maps, a completely positive trace preserving transformation and a waiting time distribution characterizing a renewal process. The relationship between this construction and a Lindblad dynamics is clarified by expressing the solution of a Lindblad master equation in terms of demixtures over different stochastic trajectories for the statistical operator weighted by suitable probabilities on the trajectory space.

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18

Sha, Linxiu, and Zhongqi Pan. "FSQGA based 3D complexity wellbore trajectory optimization." Oil & Gas Sciences and Technology – Revue d’IFP Energies nouvelles 73 (2018): 79. http://dx.doi.org/10.2516/ogst/2018008.

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Determination of the trajectory of a complex wellbore is very challenging due to the variety of possible well types, as well as the numerous complicated drilling variables and constraints. The well type could be directional wells, cluster wells, horizontal wells, extended reach wells, redrilling wells, and complex structure wells, etc. The drilling variables and constraints include wellbore length, inclination hold angles, azimuth angles, dogleg severity, true vertical depths, lateral length, casing setting depths, and true vertical depth. In this paper, we propose and develop an improved computational model based on Fibonacci sequence to adjust the quantum rotation step in quantum genetic algorithm for achieving cost-efficient complex wellbore trajectories. By using Fibonacci sequence based quantum genetic algorithm (FSQGA) in a complex searching problem, we can find high-quality globally optimal solutions with high speed through a parallel process. The simulation results show that FSQGA can significantly reduce computation complexity, and reach minimum objection values faster. Meanwhile, minimization of the true measurement depth of complex wellbore trajectory in actual gas-oil field shows that the drilling cost can be reduced up to 4.65%. We believe this new algorithm has the potential to improve drilling efficiency, to reduce the drilling time and drilling cost in real-time wellbore trajectory control.

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19

Wiseman, H. M. "Quantum trajectories and quantum measurement theory." Quantum and Semiclassical Optics: Journal of the European Optical Society Part B 8, no. 1 (February 1996): 205–22. http://dx.doi.org/10.1088/1355-5111/8/1/015.

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20

Hiley, Basil J., Maurice A. De Gosson, and Glen Dennis. "Quantum Trajectories: Dirac, Moyal and Bohm." Quanta 8, no. 1 (June 5, 2019): 11–23. http://dx.doi.org/10.12743/quanta.v8i1.84.

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We recall Dirac's early proposals to develop a description of quantum phenomena in terms of a non-commutative algebra in which he suggested a way to construct what he called quantum trajectories. Generalising these ideas, we show how they are related to weak values and explore their use in the experimental construction of quantum trajectories. We discuss covering spaces which play an essential role in accounting for the wave properties of quantum particles. We briefly point out how new mathematical techniques take us beyond Hilbert space and into a deeper structure which connects with the algebras originally introduced by Born, Heisenberg and Jordan. This enables us to bring out the geometric aspects of quantum phenomena.Quanta 2019; 8: 11–23.

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21

Huang, Jung-Jeng. "Bohm Quantum Trajectories of Scalar Field in Trans-Planckian Physics." Advances in High Energy Physics 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/312841.

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In lattice Schrödinger picture, we investigate the possible effects of trans-Planckian physics on the quantum trajectories of scalar field in de Sitter space within the framework of the pilot-wave theory of de Broglie and Bohm. For the massless minimally coupled scalar field and the Corley-Jacobson type dispersion relation with sextic correction to the standard-squared linear relation, we obtain the time evolution of vacuum state of the scalar field during slow-roll inflation. We find that there exists a transition in the evolution of the quantum trajectory from well before horizon exit to well after horizon exit, which provides a possible mechanism to solve the riddle of the smallness of the cosmological constant.

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22

Chiribella, Giulio, and Hlér Kristjánsson. "Quantum Shannon theory with superpositions of trajectories." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2225 (May 2019): 20180903. http://dx.doi.org/10.1098/rspa.2018.0903.

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Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focused on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantization where both the information and its propagation in space–time is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.

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23

Oppenheim, Jonathan, Carlo Sparaciari, Barbara Šoda, and Zachary Weller-Davies. "Objective trajectories in hybrid classical-quantum dynamics." Quantum 7 (January 3, 2023): 891. http://dx.doi.org/10.22331/q-2023-01-03-891.

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Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the back-reaction of quantum fields on space-time which does not suffer from the pathologies of the semi-classical equations. Here we introduce several toy models in which to study hybrid classical-quantum evolution, including a qubit coupled to a particle in a potential, and a quantum harmonic oscillator coupled to a classical one. We present an unravelling approach to calculate the dynamics, and provide code to numerically simulate it. Unlike the purely quantum case, the trajectories (or histories) of this unravelling can be unique, conditioned on the classical degrees of freedom for discrete realisations of the dynamics, when different jumps in the classical degrees of freedom are accompanied by the action of unique operators on the quantum system. As a result, the “measurement postulate'' of quantum theory is not needed; quantum systems become classical because they interact with a fundamentally classical field.

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24

Peter, Patrick. "Using Trajectories in Quantum Cosmology." Universe 4, no. 8 (August 15, 2018): 89. http://dx.doi.org/10.3390/universe4080089.

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Quantum cosmology based on the Wheeler De Witt equation represents a simple way to implement plausible quantum effects in a gravitational setup. In its minisuperspace version wherein one restricts attention to FLRW metrics with a single scale factor and only a few degrees of freedom describing matter, one can obtain exact solutions and thus acquire full knowledge of the wave function. Although this is the usual way to treat a quantum mechanical system, it turns out however to be essentially meaningless in a cosmological framework. Turning to a trajectory approach then provides an effective means of deriving physical consequences.

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25

Spiller, T. P., T. D. Clark, R. J. Prance, H. Prance, and D. A. Poulton. "Coherent quantum oscillation trajectories." Foundations of Physics Letters 4, no. 1 (February 1991): 19–35. http://dx.doi.org/10.1007/bf00666414.

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26

Polzik, Eugene S., and Klemens Hammerer. "Trajectories without quantum uncertainties." Annalen der Physik 527, no. 1-2 (November 11, 2014): A15—A20. http://dx.doi.org/10.1002/andp.201400099.

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27

Yang, Ciann-Dong, and Shih-Ming Huang. "Electronic quantum trajectories in a quantum dot." International Journal of Quantum Chemistry 114, no. 14 (April 22, 2014): 920–30. http://dx.doi.org/10.1002/qua.24692.

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Kumar, A., T. Krisnanda, P. Arumugam, and T. Paterek. "Nonclassical trajectories in head-on collisions." Quantum 5 (July 19, 2021): 506. http://dx.doi.org/10.22331/q-2021-07-19-506.

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Rutherford scattering is usually described by treating the projectile either classically or as quantum mechanical plane waves. Here we treat them as wave packets and study their head-on collisions with the stationary target nuclei. We simulate the quantum dynamics of this one-dimensional system and study deviations of the average quantum solution from the classical one. These deviations are traced back to the convexity properties of Coulomb potential. Finally, we sketch how these theoretical findings could be tested in experiments looking for the onset of nuclear reactions.

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29

Polley, Kritanjan, and Roger F. Loring. "Two-dimensional vibronic spectroscopy with semiclassical thermofield dynamics." Journal of Chemical Physics 156, no. 12 (March 28, 2022): 124108. http://dx.doi.org/10.1063/5.0083868.

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Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational–electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.

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Dürr, Detlef, Sheldon Goldstein, and Nino Zanghi. "Comment on "Surrealistic Bohm Trajectories"." Zeitschrift für Naturforschung A 48, no. 12 (December 1, 1993): 1261–62. http://dx.doi.org/10.1515/zna-1993-1219.

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Abstract From the perspective of orthodox quantum theory, no meaning can be assigned to the notion of the "slit" through which the atom passed in the experiments under discussion in this paper. From a Bohmian perspective this notion does have meaning. Moreover, when we compare the answer provided by BM with the answer provided, not by orthodox quantum theory, but by a naive, largely incoherent operationalism, we obtain different answers. So what?

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31

DELIS, N., C. EFTHYMIOPOULOS, and G. CONTOPOULOS. "QUANTUM VORTICES AND TRAJECTORIES IN PARTICLE DIFFRACTION." International Journal of Bifurcation and Chaos 22, no. 09 (September 2012): 1250214. http://dx.doi.org/10.1142/s0218127412502148.

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We investigate the phenomenon of the diffraction of charged particles by thin material targets using the method of the de Broglie–Bohm quantum trajectories. The particle wave function can be modeled as a sum of two terms ψ = ψ ingoing + ψ outgoing . A thin separator exists between the domains of prevalence of the ingoing and outgoing wavefunction terms. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of quantum vortices. The flow structure around each vortex displays a characteristic pattern called "nodal point–X point complex". The X point gives rise to stable and unstable manifolds. We find the scaling laws characterizing a nodal point–X point complex by a local perturbation theory around the nodal point. We then analyze the dynamical role of vortices in the emergence of the diffraction pattern. In particular, we demonstrate the abrupt deflections, along the direction of the unstable manifold, of the quantum trajectories approaching an X-point along its stable manifold. Theoretical results are compared to numerical simulations of quantum trajectories. We finally calculate the times of flight of particles following quantum trajectories from the source to detectors placed at various scattering angles θ, and thereby propose an experimental test of the de Broglie–Bohm formalism.

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32

BARCHIELLI, A., M. GREGORATTI, and M. LICCIARDO. "QUANTUM TRAJECTORIES, FEEDBACK AND SQUEEZING." International Journal of Quantum Information 06, supp01 (July 2008): 581–87. http://dx.doi.org/10.1142/s0219749908003815.

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Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light emitted by a two-level atom, stimulated by a coherent monochromatic laser. In the presence of a Wiseman-Milburn feedback scheme, based on the homodyne detection of a fraction of the emitted light, we analyze the squeezing dependence on the various control parameters.

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33

Karami, Hamid, and S. V. Mousavi. "Time-dependent potential barriers and superarrivals." Canadian Journal of Physics 93, no. 4 (April 2015): 413–17. http://dx.doi.org/10.1139/cjp-2014-0311.

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Scattering of a Gaussian wavepacket from rectangular potential barriers with increasing widths or heights is studied numerically. It is seen that during a certain time interval the time-evolving transmission probability increases compared to the corresponding unperturbed cases. In the literature this effect is known as superarrival in transmission probability. We present a trajectory-based explanation for this effect by using the concept of quantum potential energy and computing a selection of Bohmian trajectories. Relevant parameters in superarrivals are determined for the case that the barrier width increases linearly during the dispersion of the wavepacket. Nonlinearity in time perturbation is also considered.

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Anderson, Michelle C., Addison J. Schile, and David T. Limmer. "Nonadiabatic transition paths from quantum jump trajectories." Journal of Chemical Physics 157, no. 16 (October 28, 2022): 164105. http://dx.doi.org/10.1063/5.0102891.

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We present a means of studying rare reactive pathways in open quantum systems using transition path theory and ensembles of quantum jump trajectories. This approach allows for the elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. We detail the dominant pathways and rates of thermally activated processes and the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the transition state as defined through a generalization of a committor function for a thermal barrier crossing event. Similarly, the geometry changes the mechanism of relaxation following a vertical excitation. Relaxation in models resulting from small diabatic coupling proceeds through pathways dominated by pure dephasing, while those with large diabatic coupling proceed through pathways limited by dissipation. The perspective introduced here for the nonadiabatic dynamics of open quantum systems generalizes classical notions of reactive paths to fundamentally quantum mechanical processes.

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35

Robles-Pérez, Salvador J. "Quantum Cosmology in the Light of Quantum Mechanics." Galaxies 7, no. 2 (April 24, 2019): 50. http://dx.doi.org/10.3390/galaxies7020050.

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There is a formal analogy between the evolution of the universe, when it is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm, where the trajectories are transformed into wave packets that give us the probability of finding the universe or the particle in a given point of their respective spaces: the spacetime in the case of the particle and the minisuperspace in the case of the universe. The wave function of the spacetime and the matter fields, all together, can then be seen as a super-field that propagates in the minisuperspace and the so-called third quantisation procedure can be applied in a parallel way as the second quantisation procedure is performed with a matter field that propagates in the spacetime. The super-field can thus be interpreted as made up of universes propagating, i.e., evolving, in the minisuperspace. The analogy can also be used in the opposite direction. The way in which the semiclassical state of the universe is obtained in quantum cosmology allows us to obtain, from the quantum state of a field that propagates in the spacetime, the geodesics of the underlying spacetime as well as their quantum uncertainties or dispersions. This might settle a new starting point for a different quantisation of the spacetime.

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36

Daley, Andrew J. "Quantum trajectories and open many-body quantum systems." Advances in Physics 63, no. 2 (March 4, 2014): 77–149. http://dx.doi.org/10.1080/00018732.2014.933502.

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37

Griffiths, Robert B. "Consistent interpretation of quantum mechanics using quantum trajectories." Physical Review Letters 70, no. 15 (April 12, 1993): 2201–4. http://dx.doi.org/10.1103/physrevlett.70.2201.

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38

Micha, David A. "Quantum dynamics with trajectories. Introduction to quantum hydrodynamics." International Journal of Quantum Chemistry 106, no. 7 (2006): 1720. http://dx.doi.org/10.1002/qua.20945.

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39

Gersten, Alexander, and Amnon Moalem. "Quantum corrections to classical trajectories." Journal of Physics: Conference Series 1956, no. 1 (July 1, 2021): 012013. http://dx.doi.org/10.1088/1742-6596/1956/1/012013.

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40

Carrara, Nicholas. "Quantum Trajectories in Entropic Dynamics." Proceedings 33, no. 1 (December 13, 2019): 25. http://dx.doi.org/10.3390/proceedings2019033025.

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Entropic Dynamics is a framework for deriving the laws of physics from entropic inference. In an (ED) of particles, the central assumption is that particles have definite yet unknown positions. By appealing to certain symmetries, one can derive a quantum mechanics of scalar particles and particles with spin, in which the trajectories of the particles are given by a stochastic equation. This is much like Nelson’s stochastic mechanics which also assumes a fluctuating particle as the basis of the microstates. The uniqueness of ED as an entropic inference of particles allows one to continuously transition between fluctuating particles and the smooth trajectories assumed in Bohmian mechanics. In this work we explore the consequences of the ED framework by studying the trajectories of particles in the continuum between stochastic and Bohmian limits in the context of a few physical examples, which include the double slit and Stern-Gerlach experiments.

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41

Vogelsberger, S., and D. Spehner. "Entanglement evolution for quantum trajectories." Journal of Physics: Conference Series 306 (July 8, 2011): 012029. http://dx.doi.org/10.1088/1742-6596/306/1/012029.

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42

Strunz, Walter T., Lajos Diósi, Nicolas Gisin, and Ting Yu. "Quantum Trajectories for Brownian Motion." Physical Review Letters 83, no. 24 (December 13, 1999): 4909–13. http://dx.doi.org/10.1103/physrevlett.83.4909.

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43

Coffey, T. M., R. E. Wyatt, and W. C. Schieve. "Quantum trajectories from kinematic considerations." Journal of Physics A: Mathematical and Theoretical 43, no. 33 (July 13, 2010): 335301. http://dx.doi.org/10.1088/1751-8113/43/33/335301.

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44

Xu, Feng, Li-Fei Wang, and Xiao-Dong Cui. "Quantum Interference by Entangled Trajectories." Chinese Physics Letters 32, no. 8 (August 2015): 080304. http://dx.doi.org/10.1088/0256-307x/32/8/080304.

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45

Weber, Steven J., Kater W. Murch, Mollie E. Kimchi-Schwartz, Nicolas Roch, and Irfan Siddiqi. "Quantum trajectories of superconducting qubits." Comptes Rendus Physique 17, no. 7 (August 2016): 766–77. http://dx.doi.org/10.1016/j.crhy.2016.07.007.

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46

Sanz, A. S., and F. Borondo. "Contextuality, decoherence and quantum trajectories." Chemical Physics Letters 478, no. 4-6 (August 2009): 301–6. http://dx.doi.org/10.1016/j.cplett.2009.07.061.

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47

Razavy, M. "Wigner trajectories in quantum tunneling." Physics Letters A 212, no. 3 (March 1996): 119–22. http://dx.doi.org/10.1016/0375-9601(96)00030-8.

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48

Benoist, T., M. Fraas, Y. Pautrat, and C. Pellegrini. "Invariant measure for quantum trajectories." Probability Theory and Related Fields 174, no. 1-2 (July 20, 2018): 307–34. http://dx.doi.org/10.1007/s00440-018-0862-9.

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Deckert, D. A., D. Dürr, and P. Pickl. "Quantum Dynamics with Bohmian Trajectories†." Journal of Physical Chemistry A 111, no. 41 (October 2007): 10325–30. http://dx.doi.org/10.1021/jp0711996.

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Wyatt, Robert E., Courtney L. Lopreore, and Gérard Parlant. "Electronic transitions with quantum trajectories." Journal of Chemical Physics 114, no. 12 (March 22, 2001): 5113–16. http://dx.doi.org/10.1063/1.1357203.

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