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

arXiv:cond-mat/0210383 · AIP conference proceedings

Can Quantum Regression Theorem Be Reconciled with Quantum Fluctuation Dissipation Theorem ?

P. Shiktorov

Published Jan 1, 2003• 0 citations
arXivHTMLPDF

Abstract

In the attempt to derive the regression theorem from the fluctuation dissipation theorem several authors claim the violation of the former theorem in the quantum case. Here we pose the question: does it exisist a quantum fluctuation dissipation theorem (QFDT) in its conventional interpretation ? It is shown that the relation usually called as the QFDT is the condition of detailed macroscopic energetic balance. Following this interpretation the existing conflict between the two theorems in the quantum case is removed.

DOI
10.1063/1.1584937

Related papers

QUANTUM FLUCTUATION DISSIPATION THEOREM REVISITED: REMARKS AND CONTRADICTIONS

Lino Reggiani, P. Shiktorov, Evgenij Starikov +1 more

The quantum fluctuation dissipation theorem (QFDT) in the Callen–Welton [ Phys. Rev.83 (1951) 34] form is critically revisited. We show that the role of the system eigenvalues is in general not correctly accounted for by the accepted form of the QFDT. As a consequence, a series of quantum results claimed in the literature, like the presence of zero point fluctuations, the violation of the quantum regression hypothesis, the non-white spectrum of the Langevin force, etc. emerge as a consequence of an incorrect application of the theorem. In this context the case of the single harmonic oscillator is illustrated as a typical example where the accepted form of the QFDT is proven to fail.

Fluctuation and Noise Letters•Sep 1, 2012•6 citations

There is No Quantum Regression Theorem

G. W. Ford, Robert F. O’Connell

The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem.

Physical Review Letters•Jul 29, 1996•107 citations

Common Origin of Quantum Regression and Quantum Fluctuation Dissipation Theorems

P. Shiktorov, Evgenij Starikov, Viktor Gružinskis +3 more

It is shown that the quantum fluctuation dissipation theorem can be considered as a mathematical formulation in the spectral representation of Onsager hypothesis on the regression of fluctuations in physical systems. It is shown that the quantum fluctuation dissipation theorem can be generalized to an arbitrary stationary state.

arXiv:cond-mat/0011420•Nov 24, 2000•0 citations

A quantum generalization of the thermal viscous friction law

P. Shiktorov, Evgenij Starikov, Viktor Gružinskis +1 more

On the basis of the equivalence of the energy balance deacription at micro- and macro-level we propose a quantum generalization of the viscous friction law for a macroscopic Langevin equation describing thermal fluctuations without the zero point contribution. This equation recovers the classical case in the limit h -> 0. In particular it satisfies the quantum regression theorem and resolves several anomalies appearing in the quantum extension of the fluctuation dissipation theorem.

arXiv:cond-mat/0305228•May 10, 2003•0 citations

Fluctuation-dissipation theorem for nonequilibrium quantum systems

Zhedong Zhang, Wei Wu, Jin Wang

We present a fluctuation-dissipation theorem (FDT) for nonequilibrium quantum systems with detailed-balance breaking, which deviates from the conventional form of the FDT for equilibrium systems preserving detailed balance. Using the phase space formulation of quantum mechanics and the potential-flux landscape framework, we find that the response function of nonequilibrium quantum systems to external perturbations contains a nontrivial contribution from the quantum curl flux quantifying detailed-balance breaking in the steady state, in addition to the correlation function of observables in the steady state representing the contribution of spontaneous fluctuations which is also present in the equilibrium FDT. We illustrate our general formalism with a harmonic oscillator coupled to two heat baths, and show that the nonequilibrium FDT reduces to the conventional expression at the equilibrium condition when the flux contribution vanishes.

Europhysics Letters (EPL)•Jul 1, 2016•7 citations

Quantum violation of fluctuation-dissipation theorem

Akira Shimizu, Kyota Fujikura

Abstract We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a ‘squeezed equilibrium state’, which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.

arXiv:1610.03161•Journal of Statistical Mechanics Theory and Experiment•Feb 1, 2017•16 citations
In the attempt to derive the regression theorem from the fluctuation dissipation theorem several authors claim the violation of the former theorem in the quantum case. Here we pose the question: does it exisist a quantum fluctuation dissipation theorem (QFDT) in its conventional interpretation ? It is shown that the relation usually called as the QFDT is the condition of detailed macroscopic energetic balance. Following this interpretation the existing conflict between the two theorems in the quantum case is removed.
The quantum fluctuation dissipation theorem (QFDT) in the Callen–Welton [ Phys. Rev.83 (1951) 34] form is critically revisited. We show that the role of the system eigenvalues is in general not correctly accounted for by the accepted form of the QFDT. As a consequence, a series of quantum results claimed in the literature, like the presence of zero point fluctuations, the violation of the quantum regression hypothesis, the non-white spectrum of the Langevin force, etc. emerge as a consequence of an incorrect application of the theorem. In this context the case of the single harmonic oscillator is illustrated as a typical example where the accepted form of the QFDT is proven to fail.
We present a fluctuation-dissipation theorem (FDT) for nonequilibrium quantum systems with detailed-balance breaking, which deviates from the conventional form of the FDT for equilibrium systems preserving detailed balance. Using the phase space formulation of quantum mechanics and the potential-flux landscape framework, we find that the response function of nonequilibrium quantum systems to external perturbations contains a nontrivial contribution from the quantum curl flux quantifying detailed-balance breaking in the steady state, in addition to the correlation function of observables in the steady state representing the contribution of spontaneous fluctuations which is also present in the equilibrium FDT. We illustrate our general formalism with a harmonic oscillator coupled to two heat baths, and show that the nonequilibrium FDT reduces to the conventional expression at the equilibrium condition when the flux contribution vanishes.
Abstract We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a ‘squeezed equilibrium state’, which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.