# Exact Markovian kinetic equation for a quantum Brownian oscillator.

@article{Tay2006ExactMK, title={Exact Markovian kinetic equation for a quantum Brownian oscillator.}, author={B. A. Tay and G. Ordonez}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2006}, volume={73 1 Pt 2}, pages={ 016120 } }

We derive an exact Markovian kinetic equation for an oscillator linearly coupled to a heat bath, describing quantum Brownian motion. Our work is based on the subdynamics formulation developed by Prigogine and collaborators. The space of distribution functions is decomposed into independent subspaces that remain invariant under Liouville dynamics. For integrable systems in Poincaré's sense the invariant subspaces follow the dynamics of uncoupled, renormalized particles. In contrast, for… Expand

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#### References

SHOWING 1-10 OF 28 REFERENCES

Kinetic equations from Hamiltonian dynamics: Markovian limits

- Physics
- 1980

Dynamical processes in macroscopic systems are often approximately described by kinetic and hydrodynamic equations. One of the central problems in nonequilibrium statistical mechanics is to… Expand

Star-unitary transformations: from dynamics to irreversibility and stochastic behavior.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2003

This paper presents a formulation in terms of dressed particles, which gives exact Markovian equations for Poincaré nonintegrable systems, through an invertible transformation operator Lambda introduced by Prigogine and co-workers, and shows that Lambda-transformed variables have the same time evolution as stochastic variables obeying Langevin equations. Expand

Quantum theory of non-integrable systems

- Mathematics
- 1991

In 1889 H. Poincare introduced a basic distinction between integrable and non-integrable dynamical systems. This distinction refers to the role of resonances which may lead to divergences. A… Expand

Quantum decoherence, Zeno process, and time symmetry breaking.

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

The essential element in the understanding of quantum decoherence is the "extensivity" of quantities characterizing the thermodynamic limit. Expand

Radiation damping in classical systems: The role of nonintegrability

- Physics
- 2003

The interaction between matter and fields is a classical problem. Still there are difficulties. Time symmetry is broken. So the radiation damping belongs to a class of phenomena, which includes… Expand

Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1992

The influence functional path-integral method is used to derive an exact master equation for the quantum Brownian motion of a particle linearly coupled to a general environment at arbitrary temperature and applies it to study certain aspects of the loss of quantum coherence. Expand

Thermodynamics and small quantum systems

- Physics
- 2003

Abstract Small quantum systems non-weakly coupled to a bath become in the quantum regime surrounded by a cloud of photons or phonons, which modifies their thermodynamic behaviour. Exactly solvable… Expand

Collision operator in the physical representation, the Friedrichs model

- Mathematics
- 1973

Recent work by the Brussels group has shown the importance of parity properties of the dynamical operators for large systems with respect to the inversion L → -L, L being the Liouville-Von Neumann… Expand

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… Expand

Classical and quantum mechanics of the damped harmonic oscillator

- Physics
- 1981

Abstract The relations between various treatments of the classical linearly damped harmonic oscillator and its quantization are investigated. In the course of a historical survey typical features of… Expand