Seven steps towards the classical world

Allori, Valia; Dürr, Detlef; Goldstein, Shelly; Zanghı̀, Nino

doi:10.1088/1464-4266/4/4/344

Cited by 48 publications

(65 citation statements)

References 11 publications

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“…This should not be confused with the physically much deeper question of how our everyday world of objects moving along single trajectories emerges out of quantum mechanics; this question is addressed, e.g., in Ref. [38]. We will adopt a part of the argumentation given in the latter reference to answer the simpler question that we are concerned with here.…”

Section: The Classical Limit As a Scaling Limitmentioning

confidence: 99%

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Towards a variational formulation of mixed quantum-classical molecular dynamics

Römer

Burghardt

2013

Molecular Physics

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A variational formulation of mixed quantum-classical dynamics is proposed, based upon a wave function form of Gaussianbased multiconfiguration time-dependent Hartree (G-MCTDH) type. Using semiclassically scaled Gaussian wave packets that lead to a classical evolution in an appropriate limit, a multiconfigurational Ehrenfest dynamics is obtained. Due to the variational framework, the resulting quantum-classical dynamics is consistent and accounts for correlations between the quantum and classical subspaces.

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Section: The Classical Limit As a Scaling Limitmentioning

confidence: 99%

“…Moreover, we are interested in dynamics where the momentum is of order one, i.e. p = m(dx/dt) = m(dy/d(εt)) ∼ 1, so we also have to rescale the time variable [38,44]. We denote the scaled time by s = εt.…”

Section: The Classical Limit As a Scaling Limitmentioning

confidence: 99%

Towards a variational formulation of mixed quantum-classical molecular dynamics

Römer

Burghardt

2013

Molecular Physics

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“…The issue was formerly discussed by Allori et al [342], who claimed that Bohmian mechanics constitutes, precisely, the correct way to recover the classical limit. This limit should be essentially analogous to determine when Bohmian trajectories look Newtonian, but in a rather different fashion to other attempts based on the standard conception of correspondence of simply varying a certain control parameter.…”

Section: Role Of Entanglement and Decoherencementioning

confidence: 99%

Applied Bohmian Mechanics

Oriols¹,

Mompart²

2012

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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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“…To be sure: this does not imply that a typical Bohmian trajectory stays close to the classical trajectory for the whole duration of a given time interval, since it may every now and then make a large excursion. We shall consider a sufficiently smooth potential and a special class of initial wave functions where the potential V varies on a much larger scale than the wave functions, see, e.g., [1] for a physical discussions of the scales. More precisely, we choose V ε (y) := V (εy) for some small parameter ε, thus defining a microscopic (y, s) and a macroscopic scale (x, t) := (εy, εs).…”

Section: Introductionmentioning

confidence: 99%