Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Nuclear Physics B - Proceedings Supplements

Quantum brownian motion, irreversibility and non-equilibrium stationary states

Hiroshi Nakazawa

Published Sep 1, 1988• 0 citations
Publisher
DOI
10.1016/0920-5632(88)90051-5

Related papers

Quantum Brownian motion and its conflict with the second law

Theo M. Nieuwenhuizen

The Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non‐Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non‐adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics.

arXiv:cond-mat/0208564•AIP conference proceedings•Jan 1, 2002•2 citations

Quantum Brownian Motion. II

Fabián H. Gaioli, Edgardo T. Garcia Alvarez, Diego G. Arbo

arXiv:quant-ph/9807049•International Journal of Theoretical Physics•Jan 1, 1999•3 citations

Quantum Brownian Motion Revisited

Aniello Lampo, Miguel Ángel García March, Maciej Lewenstein

SpringerBriefs in physics•Jan 1, 2019•18 citations

Quantum Einstein's Brownian Motion

Roumen Tsekov

Einstein's Brownian motion of a quantum particle in a classical environment is studied via virial and equipartition theorems. The effect of continuous measurement in a strongly dissipative environment is accounted for and a quantum generalization of the classical Einstein law of Brownian motion is obtained. A thermo-quantum Smoluchowski diffusion equation is derived via a generalization of the Madelung quantum hydrodynamics. The latter is applied for description of the quantum tunneling at equilibrium and stationary states as well as of the motion of an electron in metals, i.e. the Smoluchowski-Poisson problem.

arXiv:1001.3093•Jan 18, 2010•1 citation

Quantum Brownian Motion

Aniello Lampo, Miguel Ángel García March, Maciej Lewenstein

SpringerBriefs in physics•Jan 1, 2019•3 citations

Can the Schrodinger dynamics explain measurement?

Alexey A. Kryukov

The motion of a ball through an appropriate lattice of round obstacles models the behavior of a Brownian particle and can be used to describe measurement on a macro system. On another hand, such motion is chaotic and a known conjecture asserts that the Hamiltonian of the corresponding quantum system must follow the random matrix statistics of an appropriate ensemble. We use the Hamiltonian represented by a random matrix in the Gaussian unitary ensemble to study the Schrödinger evolution of non-stationary states. For Gaussian states representing a classical system, the Brownian motion that describes the behavior of the system under measurement is obtained. For general quantum states, the Born rule for the probability of transition between states is derived. It is then shown that the Schrödinger evolution with such a Hamiltonian models measurement on macroscopic and microscopic systems, provides an explanation for the classical behavior of macroscopic bodies and for irreversibility of a measurement, and identifies the boundary between micro and macro worlds.

arXiv:2301.01858•Jan 5, 2023•0 citations
The Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non‐Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non‐adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics.
Einstein's Brownian motion of a quantum particle in a classical environment is studied via virial and equipartition theorems. The effect of continuous measurement in a strongly dissipative environment is accounted for and a quantum generalization of the classical Einstein law of Brownian motion is obtained. A thermo-quantum Smoluchowski diffusion equation is derived via a generalization of the Madelung quantum hydrodynamics. The latter is applied for description of the quantum tunneling at equilibrium and stationary states as well as of the motion of an electron in metals, i.e. the Smoluchowski-Poisson problem.
The motion of a ball through an appropriate lattice of round obstacles models the behavior of a Brownian particle and can be used to describe measurement on a macro system. On another hand, such motion is chaotic and a known conjecture asserts that the Hamiltonian of the corresponding quantum system must follow the random matrix statistics of an appropriate ensemble. We use the Hamiltonian represented by a random matrix in the Gaussian unitary ensemble to study the Schrödinger evolution of non-stationary states. For Gaussian states representing a classical system, the Brownian motion that describes the behavior of the system under measurement is obtained. For general quantum states, the Born rule for the probability of transition between states is derived. It is then shown that the Schrödinger evolution with such a Hamiltonian models measurement on macroscopic and microscopic systems, provides an explanation for the classical behavior of macroscopic bodies and for irreversibility of a measurement, and identifies the boundary between micro and macro worlds.