# The status of the quantum dissipation–fluctuation relation and the Langevin equation

@article{Taylor2007TheSO, title={The status of the quantum dissipation–fluctuation relation and the Langevin equation}, author={J. C. Taylor}, journal={Journal of Physics: Condensed Matter}, year={2007}, volume={19}, pages={106223} }

I examine the arguments which have been given for quantum fluctuation?dissipation theorems. I distinguish between a weak form of the theorem, which is true under rather general conditions, and a strong form which requires a Langevin equation for its statement. I argue that the latter has not been reliably derived in general.

#### 7 Citations

Conditions for the validity of the quantum Langevin equation.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2012

This work bases its discussion on a direct, elementary treatment of Senitzky via a generalized Langevin equation as an intermediate step, and test this method by comparison with an exactly soluble model and point out its limitations. Expand

Under which conditions is quantum Brownian motion observable in a microscope

- Physics
- 2010

Abstract We investigate under which conditions we can expect to observe quantum Brownian motion in a microscope. Using the fluctuation–dissipation theorem, we investigate quantum Brownian motion in… Expand

Brownian motion, quantum corrections and a generalization of the Hermite polynomials

- Computer Science, Mathematics
- J. Comput. Appl. Math.
- 2010

The approximate nonequilibrium theory yields irreversible evolution of the Brownian particle towards thermal equilibrium with the ''heat bath'' and a new family of orthogonal polynomials which generalize the Hermite ones is introduced. Expand

Nonequilibrium quantum anharmonic oscillator and scalar field: high temperature approximations

- Physics
- 2009

We treat a relativistic quantum boson gas, described by a scalar quantum field, with quartic self-interaction (ϕ4) in three spatial dimensions: we review the known equilibrium case and present new… Expand

Mapping fermion and boson systems onto the Fock space of harmonic oscillators.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2010

It is shown that, whenever linear response theory applies, any generic bosonic or fermionic system at finite temperature T can be mapped onto a fictitious system of free-harmonic oscillators, the first time that such a mapping is explicitly worked out. Expand

ELECTROMAGNETIC DARK ENERGY

- Physics
- 2008

We introduce a new model for dark energy in the Universe in which a small cosmological constant is generated by ordinary electromagnetic vacuum energy. The corresponding virtual photons exist at all… Expand

Dark energy and Josephson junctions

- Physics
- 2009

It has been recently claimed that dark energy can be (and has been) observed in laboratory experiments by measuring the power spectrum SI(ω) of the noise current in a resistively shunted Josephson… Expand

#### References

SHOWING 1-10 OF 20 REFERENCES

On a quasiclassical Langevin equation

- Physics
- 1982

It is shown that the motion of a quantum mechanical particle coupled to a dissipative environment can be described by a Langevin equation where the stochastic force is generalized such that its power… Expand

DAMPING AND NOISE IN QUANTUM MECHANICS

- Physics
- 2001

In a quantum system damping and noise enter through the coupling with an external large bath. The usual treatments computes the density matrix of the system by expanding in the coupling strength to… Expand

Irreversibility and Generalized Noise

- Physics
- 1951

A relation is obtained between the generalized resistance and the fluctuations of the generalized forces in linear dissipative systems. This relation forms the extension of the Nyquist relation for… Expand

Dissipation in Quantum Mechanics. The Harmonic Oscillator

- Physics
- 1960

The need for a quantum-mechanical formalism for systems with dissipation which is applicable to the radiation field of a cavity is discussed. Two methods that have been used in this connection are… Expand

Quantum noise in a current-biased Josephson junction

- Physics
- 2003

Quantum fluctuations in a current-biased Josephson junction, described in terms of the RCSJ model, are considered. The fluctuations of the voltage and phase across the junction are assumed to be… Expand

Detection of quantum noise

- Physics
- 2000

We discuss the detection of quantum fluctuations in the light of the relationship between time-dependent correlators and measurable properties [L. Van Hove, Phys. Rev 95, 249 (1954)]. Considering the… Expand

Electronic noise and fluctuations in solids

- Physics, Engineering
- 1996

This book looks at the physics of electronic fluctuations (noise) in solids. The author emphasizes many fundamental experiments that have become classics: physical mechanisms of fluctuations, and the… Expand

Could dark energy be measured in the lab

- Physics
- 2005

The experimentally measured spectral density of current noise in Josephson junctions provides direct evidence for the existence of zero-point fluctuations. Assuming that the total vacuum energy… Expand

Measurements of quantum noise in resistively shunted Josephson junctions

- Physics
- 1982

Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down… Expand

Fluctuation and Noise Letters

- 2007

Parrondo’s paradox [1–4] shows that the combination of two losing strategies can lead to a winning result. The paradox can be phrased in terms of very simple gambling games in which some unit (say, 1… Expand