Theory of open quantum systems

@article{Xu2002TheoryOO,
  title={Theory of open quantum systems},
  author={Ruixue Xu and Yijing Yan},
  journal={Journal of Chemical Physics},
  year={2002},
  volume={116},
  pages={9196-9206}
}
A quantum dissipation theory is constructed with the system–bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition. The theory is valid for arbitrary bath correlation functions and time-dependent external driving fields, and satisfies correlated detailed-balance relation at any temperatures. The general formulation assumes a particularly simple form in driven Brownian oscillator systems in which the… 

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References

SHOWING 1-10 OF 40 REFERENCES
Cavity quantum electrodynamics in the presence of energy relaxation and pure dephasing: A unified quantum master-equation approach
This paper renders two main results. One is a unified quantum master equation, which satisfies the detailed-balance relation and can serve as a convenient starting formulation to study the
Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath
A test system is assumed to interact with a heat bath consisting of harmonic oscillators or an equivalent bath with a proper frequency spectrum producing a Gaussian-Markoffian random perturbation.
A phase-space study of Bloch–Redfield theory
A phase-space representation of Bloch–Redfield theory is used to describe the dynamical evolution of quantum dissipative systems. The resulting Liouville operator equations are capable of
Quantum Fokker-Planck theory in a non-Gaussian-Markovian medium
We develop a generalized quantum Fokker-Planck theory in a non-Gaussian-Markovian model bath. The semiclassical bath adopted in this work is charactered by three parameters. One denotes the strength
Quantum Dissipative Systems
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
On Quantum Theory of Transport Phenomena Steady Diffusion
A general formulation is given to the quantum theory of steady diffusion. In seeking for a steady solution of Liouville's equation, the boundary condition is taken into account by requiring that the
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
Phase space approach to theories of quantum dissipation
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,
Unified approach to the Bloch–Redfield theory and quantum Fokker–Planck equations
By using a rather simple algebraic approach, we revisit and further bridge between two most commonly used quantum dissipation theories, the Bloch–Redfield theory and a class of Fokker–Planck
Markovian master equations
We give a rigorous proof that under certain technical conditions the memory effects in a quantum-mechanical master equation become negligible in the weak coupling limit. This is sufficient to show
...
1
2
3
4
...