Quantum potential and random phase-space dynamics

Czopnik, R.; Garbaczewski, Piotr

doi:10.1016/s0375-9601(02)00757-0

Physics Letters A

2002

DOI: 10.1016/s0375-9601(02)00757-0

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Quantum potential and random phase-space dynamics

R. Czopnik

Piotr Garbaczewski

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Cited by 4 publications

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“…The energy conservation during the collisions considered in the present scheme plays a very important role and could be also taken into account in the stochastic models of quantum mechanics as it has been recently observed in ref. [3].…”

mentioning

confidence: 99%

BBGKY hierarchy underlying many-particle quantum mechanics

Kaniadakis

2003

Physics Letters A

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Recently, the one particle quantum mechanics has been obtained in the framework of an entirely classical subquantum kinetics. In the present paper we argue that, within the same scheme and without any additional assumption, it is possible to obtain also the n-particle non relativistic quantum mechanics. The main goal of the present effort is to show that the classical BBGKY hierarchical equation, for the n-particle reduced distribution function, is the ancestor of the n-particle Schrödinger equation. On the other hand we show that within the scenario of the subquantum structure of quantum particle, the Fisher information measure emerges naturally in quantum mechanics.

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confidence: 99%

BBGKY hierarchy underlying many-particle quantum mechanics

Kaniadakis

2003

Physics Letters A

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Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond

Ván

2006

Physica A: Statistical Mechanics and its Applications

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It is proved that the only additive and isotropic information measure that can depend on the probability distribution and also on its first derivative is a linear combination of the Boltzmann-Gibbs-Shannon and Fisher information measures. Power law equilibrium distributions are found as a result of the interaction of the two terms. The case of second order derivative dependence is investigated and a corresponding additive information measure is given.

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Nonlinear Ginzburg-Landau-type approach to quantum dissipation

López

2004

Phys. Rev. E

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We formally derive two nonlinear Ginzburg-Landau type models starting from the Wigner-Fokker-Planck system, which rules the evolution of a quantum electron gas interacting with a heat bath in thermodynamic equilibrium. These models mainly consist of a quantum, dissipative O(Planck 3) hydrodynamic/O(Planck 4) stochastic correction to the frictional (Caldeira-Leggett-)Schrödinger equation. The main ingredient lies in the use of the hydrodynamic/stochastic fluid model approach associated with the quantum Fokker-Planck equation and the identification of the associated pressure field. Then, Madelung transformations set the problem in the Schrödinger picture of dissipative quantum mechanics. We also describe the stationary dynamics associated with both systems.

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Quantum potential and random phase-space dynamics

Cited by 4 publications

References 15 publications

BBGKY hierarchy underlying many-particle quantum mechanics

BBGKY hierarchy underlying many-particle quantum mechanics

Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond

Nonlinear Ginzburg-Landau-type approach to quantum dissipation

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