Hydrodynamic View of Wave-Packet Interference: Quantum Caves

Chou, Chia‐Chun; Sanz, Ángel S.; Miret‐Artés, Salvador; Wyatt, Róbert E.

doi:10.1103/physrevlett.102.250401

Cited by 51 publications

(54 citation statements)

References 24 publications

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“…Later on this modified de BroglieBohm approach, as denoted by John, has also been applied to the analysis of the Born rule and the normalization conditions of the probability density in the complex plane [374,375], or the dynamics of coherent states [376,377]. Analogous studies carried out to determine different dynamical properties with this complex Bohmian representation have been carried out extensively in the literature [349,[378][379][380][381][382][383][384][385][386][387][388][389][390][391][392][393][394][395][396][397].…”

Section: Trajectories From Complex Actionmentioning

confidence: 99%

Applied Bohmian mechanics

et al. 2014

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Abstract. Bohmian mechanics provides an explanation of quantum phenomena in terms of point-like particles guided by wave functions. This review focuses on the use of nonrelativistic Bohmian mechanics to address practical problems, rather than on its interpretation. Although the Bohmian and standard quantum theories have different formalisms, both give exactly the same predictions for all phenomena. Fifteen years ago, the quantum chemistry community began to study the practical usefulness of Bohmian mechanics. Since then, the scientific community has mainly applied it to study the (unitary) evolution of single-particle wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectorybased explanation of complicated quantum phenomena. Here we present a large list of examples showing how the Bohmian formalism provides a useful solution in different forefront research fields for this kind of problems (where the Bohmian and the quantum hydrodynamic formalisms coincide). In addition, this work also emphasizes that the Bohmian formalism can be a useful tool in other types of (nonunitary and nonlinear) quantum problems where the influence of the environment or the nonsimulated degrees of freedom are relevant. This review contains also examples on the use of the Bohmian formalism for the many-body problem, decoherence and measurement processes. The ability of the Bohmian formalism to analyze this last type of problems for (open) quantum systems remains mainly unexplored by the scientific community. The authors of this review are convinced that the final status of the Bohmian theory among the scientific community will be greatly influenced by its potential success in those types of problems that present nonunitary and/or nonlinear quantum evolutions. A brief introduction of the Bohmian formalism and some of its extensions are presented in the last part of this review.

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Section: Trajectories From Complex Actionmentioning

confidence: 99%

Applied Bohmian mechanics

et al. 2014

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“…For this reason over the years numerous schemes have been proposed to a e-mail: matone@pd.infn.it address such issues. Among those, the quantum HamiltonJacobi (HJ) theory is one of the most investigated topics; see [1][2][3][4][5][6][7][8] for a partial list of papers. These studies involve the foundation of quantum mechanics, in particular its interpretation, cosmology, the analysis of quantum dynamics, molecular trajectories, etc.…”

Section: Introductionmentioning

confidence: 99%

Energy quantisation and time parameterisation

Faraggi

Matone

2014

Eur. Phys. J. C

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We show that if space is compact, then trajectories cannot be defined in the framework of the quantum Hamilton-Jacobi (HJ) equation. The starting point is the simple observation that when the energy is quantised it is not possible to make variations with respect to the energy, and the time parameterisation t − t 0 = ∂ E S 0 , implied by Jacobi's theorem, which leads to the group velocity, is ill defined. It should be stressed that this follows directly from the quantum HJ equation without any axiomatic assumption concerning the standard formulation of quantum mechanics. This provides a stringent connection between the quantum HJ equation and the Copenhagen interpretation. Together with tunnelling and the energy quantisation theorem for confining potentials, formulated in the framework of quantum HJ equation, it leads to the main features of the axioms of quantum mechanics from a unique geometrical principle. Similar to the case of the classical HJ equation, this fixes its quantum analog by requiring that there exist point transformations, rather than canonical ones, leading to the trivial hamiltonian. This is equivalent to a basic cocycle condition on the states. Such a cocycle condition can be implemented on compact spaces, so that continuous energy spectra are allowed only as a limiting case. Remarkably, a compact space would also imply that the Dirac and von Neumann formulations of quantum mechanics essentially coincide. We suggest that there is a definition of time parameterisation leading to trajectories in the context of the quantum HJ equation having the probabilistic interpretation of the Copenhagen School.

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“…[46,47] Quantum interference effects are demonstrated within the Bohmian formalism. [48,49] Bohm's analytic route is applied to solve problems related to surface science. [50,51] Dynamics of electron nonadiabatic transitions are studied within a quantum trajectory formalism.…”

Section: Quantum Fluid Dynamicsmentioning

confidence: 99%

Density dynamics in some quantum systems

Khatua

Chakraborty

Chattaraj

2013

Int J of Quantum Chemistry

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The quantum domain behavior of classical nonintegrable systems is well-understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the quantum analogs of the classical Kolmogorov-Arnold-Moser type transitions from regular to chaotic domain in different anharmonic oscillators. Field-induced tunneling and chaotic ionization in Rydberg atoms are also analyzed with the help of these theories.Quantum fluid density functional theory may be used to understand different time-dependent processes like ion-atom/ molecule collisions, atom-field interactions, and so forth. Regioselectivity as well as confined atomic/molecular systems and their reactivity dynamics have also been explained.

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Hydrodynamic View of Wave-Packet Interference: Quantum Caves

Cited by 51 publications

References 24 publications

Applied Bohmian mechanics

Applied Bohmian mechanics

Energy quantisation and time parameterisation

Density dynamics in some quantum systems

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