# Universality of quantum Brownian motion

@article{Lutz1999UniversalityOQ, title={Universality of quantum Brownian motion}, author={Eric Lutz and Hans A. Weidenmueller}, journal={Physica A-statistical Mechanics and Its Applications}, year={1999}, volume={267}, pages={354-374} }

Are Markovian master equations for quantum Brownian motion independent of model assumptions used in the derivation and, thus, universal? With the aim of answering this question, we use a random band-matrix model for the system-bath interaction to derive Markovian master equations for the time evolution of one-dimensional quantum systems weakly coupled to a heat bath. We study in detail two simple systems, the harmonic oscillator and the two-level system. Our results are in complete agreement…

## 28 Citations

Random-matrix model for quantum Brownian motion

- Physics
- 2001

Abstract We use a random band-matrix model for the system–bath interaction to derive a Markovian master equation for the time evolution of one-dimensional quantum systems weakly coupled to a heat…

Quantum kicked harmonic oscillator in contact with a heat bath

- Physics
- 2017

We consider the quantum harmonic oscillator in contact with a finite temperature bath, modelled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system…

Dynamics of complex quantum systems: dissipation and kinetic equations

- Physics
- 2001

Abstract We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex…

Kinetic theory for quantum nanosystems

- Physics
- 2004

In this thesis, we investigate the emergence of kinetic processes in finite quantum systems. We first generalize the Redfield theory to describe the dynamics of a small quantum system weakly…

A general and solvable random matrix model for spin decoherence

- Physics, Mathematics
- 2011

We propose and solve a simple but very general quantum model of a SU(2) spin interacting with a large external system with N states. The coupling is described by a random Hamiltonian in a new general…

Collective versus Single--Particle Motion in Quantum Many--Body Systems from the Perspective of an Integrable Model

- Physics, Mathematics
- 2009

We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the…

Fourier's Law for Quasi One-Dimensional Chaotic Quantum Systems

- Physics
- 2011

We derive Fourier's law for a completely coherent quasi-one-dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order…

Measuring the Lyapunov exponent using quantum mechanics.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

It is shown that for sufficiently weak perturbations, the exponential decay follows a Fermi golden rule, while by making the difference between the two Hamiltonians larger, the characteristic exponential decay time becomes the Lyapunov exponent of the classical system.

Exotic stochastic processes from quantum chaotic environments

- Physics
- 2001

Abstract Stochastic processes are shown to emerge from the time evolution of complex quantum systems. Using parametric, banded random matrix ensembles to describe a quantum chaotic environment, we…

Decoherence in chaotic and integrable systems: a random matrix approach

- Physics
- 2001

Abstract We study the influence of chaos and order on entanglement and decoherence. In view of applications in quantum computing and teleportation which should be able to work with arbitrarily…

## References

SHOWING 1-10 OF 54 REFERENCES

Path integral approach to quantum Brownian motion

- Physics, Mathematics
- 1982

We apply the influence-functional method of Feynman and Vernon to the study of Brownian motion at arbitrary temperature. By choosing a specific model for the dissipative interaction of the system of…

Dynamics of a simple quantum system in a complex environment

- Mathematics, Physics
- 1998

We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random…

Time behavior of the correlation functions in a simple dissipative quantum model

- Physics
- 1985

The force and velocity correlation functions for a particle interacting with a bath are calculated within a model allowing for finite memory effects. The relevance of a Brownian picture is delineated…

Brownian Motion of a Quantum Oscillator

- Physics
- 1971

The theory of Brownian motion of a quantum oscillator is developed. The Brownian motion is described by a model Hamiltonian which is taken to be the one describing the interaction between this…

Reduction of a wave packet in quantum Brownian motion.

- Physics, MedicinePhysical review. D, Particles and fields
- 1989

In an open quantum system, dissipation can cause decorrelation on a time scale significantly shorter than the relaxation time which characterizes the approach of the system to thermodynamic equilibrium, and it is demonstrated that the density matrix decays rapidly toward a mixture of ``approximate eigenstates'' of the ``pointer observable,'' which commutes with the system-environment interaction Hamiltonian.

Phase space approach to theories of quantum dissipation

- Chemistry
- 1997

Six major theories of quantum dissipative dynamics are compared: Redfield theory, the Gaussian phase space ansatz of Yan and Mukamel, the master equations of Agarwal,…

Quantum Brownian motion

- Physics
- 1987

Techniques for deriving the equations of motion for a heavy particle immersed in a bath of light particles have been developed for quantum systems as long as the temperature is not too low. To lowest…

Random-matrix model for dissipative two-level systems

- Mathematics
- 1991

Assuming a random-matrix model for the system-bath interaction and using a series expansion for the evolution operator, we studied the relaxation of a nondegenerate two-level system. For times larger…

On the Theory of Relaxation Processes

- Physics, Computer ScienceIBM J. Res. Dev.
- 1957

The theory is applied to spin-lattice relaxation of a coupled nuclear spin system in a metal, for arbitrary externally applied fixed magnetic field.

Quantum Dissipative Systems

- Physics
- 1993

Fundamentals Survey of the Various Approaches Path Integral Description of Open Quantum Systems Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic…