Implications of protective measurement on de Broglie–Bohm trajectories

Drezet, Aurélien

doi:10.1017/cbo9781107706927.013

Cited by 5 publications

(8 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, we restrict ourselves to the nonrelativistic Newtonian framework and unravel the emergence of a transparency regime in which the particle-string interaction, and thus the radiation force, vanish. As we show, this regime is reminiscent of de Broglie's double solution [3] (for recent works and reviews see [18][19][20]) and furthermore leads to a Schrödinger equation for the phase wave associated to the particle. Very interestingly, two classes of transparent particles are possible candidates: (i) the class of subsonic particles that FIG.…”

Section: Introductionmentioning

confidence: 66%

Mechanical analog of quantum bradyons and tachyons

et al. 2020

Self Cite

View full text Add to dashboard Cite

We present a mechanical analog of a quantum wave-particle duality: a vibrating string threaded through a freely moving bead or "masslet." For small string amplitudes, the particle movement is governed by a set of nonlinear dynamical equations that couple the wave field to the masslet dynamics. Under specific conditions, the particle achieves a regime of transparency in which the field and the particle's dynamics appear decoupled. In that special case, the particle conserves its momentum and a guiding wave obeying a Klein-Gordon equation, with real or imaginary mass, emerges. Similar to the double-solution theory of de Broglie, this guiding wave is locked in phase with a modulating group wave comoving with the particle. Interestingly, both subsonic and supersonic particles can fall into a quantum regime as is the case with the slower-than-light bradyons and hypothetical, faster-than-light tachyons of particle physics.

show abstract

Section: Introductionmentioning

confidence: 66%

Mechanical analog of quantum bradyons and tachyons

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…As pointed out by Michael Berry [312], the limit → 0 is singular (and "pathological"). To illustrate this fact in a simple manner, we are going to consider a system that has already been used in a similar fashion in different contexts [313,314], namely the particle in a one-dimensional square infinite well of size L. The eigenfunctions are of the form…”

Section: "Traditional" Classical Limitsmentioning

confidence: 99%

Applied Bohmian mechanics

et al. 2014

View full text Add to dashboard Cite

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.

show abstract

“…This is clearly reminiscent of the double-solution program developed by de Broglie [22,23]. More precisely, in the double solution of de Broglie one postulates the existence of a physical u−field guiding the particle considered as a localized 'accident' in the wave (i.e., a singularity [27]). Our model is more specific than the one proposed by de Broglie.…”

Section: Perspectives and Conclusionmentioning

confidence: 97%

A mechanical analog of Bohr's atom based on de Broglie's double-solution approach

Jamet,

Drezet

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We provide a relativistic model for a classical particle coupled to a scalar wave-field through a holonomic constraint. In presence of an external Coulomb field we define a regime where the particle is guided by the wave in a way similar to the old de Broglie phase-wave proposal. Moreover, this dualistic mechanical analog of the quantum theory is reminiscent of the double-solution approach suggested by de Broglie in 1927 and is able to reproduce the Bohr-Sommerfeld semiclassical quantization formula for an electron moving in a atom.

show abstract

Implications of protective measurement on de Broglie–Bohm trajectories

Abstract: PACS numbers:1 MOTIVATIONS

Cited by 5 publications

References 38 publications

Mechanical analog of quantum bradyons and tachyons

Mechanical analog of quantum bradyons and tachyons

Applied Bohmian mechanics

A mechanical analog of Bohr's atom based on de Broglie's double-solution approach

Contact Info

Product

Resources

About