Brownian motion of quantum harmonic oscillators: Existence of a subdynamics

@article{Lindblad1998BrownianMO,
  title={Brownian motion of quantum harmonic oscillators: Existence of a subdynamics},
  author={G{\"o}ran Lindblad},
  journal={Journal of Mathematical Physics},
  year={1998},
  volume={39},
  pages={2763-2780}
}
  • G. Lindblad
  • Published 23 October 1998
  • Physics
  • Journal of Mathematical Physics
The effects of system-environment correlations on the dynamics of an open quantum system are investigated for the standard model of a set of quantum harmonic oscillators interacting with a heat bath of oscillators. By definition, a subdynamics is described by transformations of the open system observables. It is shown that such a construction can reproduce the observable properties of the exact dynamics only when the states of system and environment are uncorrelated, while for classical systems… 
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References

SHOWING 1-10 OF 69 REFERENCES
Open quantum systems
The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion
Low-temperature and long-time anomalies of a damped quantum particle
The time evolution of a damped quantum particle is discussed. Dissipation is modeled by the bilinear coupling to a set of harmonic oscillators. Using a functional integral technique that accounts for
Low temperature equilibrium correlation functions in dissipative quantum systems
We introduce a new theoretical approach to dissipative quantum systems. By means of a continuous sequence of infinitesimal unitary transformations, we decouple the small quantum system that one is
Exact results for a damped quantum-mechanical harmonic oscillator.
TLDR
The commonly used form of Ehrenfest's equation for the dynamics of the linearly damped oscillator is shown to only be a reasonable approximation within certain frequency regimes.
Quantum Dynamical Semigroups and Applications
In this text the authors develop quantum dynamics of open systems for a wide class of irreversible processes starting from the concept of completely positive semigroups. This unified approach makes
Memory effects in the relaxation of quantum open systems
A close examination of the validity of the Markovian approximation in the context of relaxation theory is presented. In particular, we examine the question of positivity of various approximations to
An Introduction to Quantum Stochastic Calculus
"Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." - The
...
...