# 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…

## 1,584 Citations

Dynamics of quantum dissipation systems interacting with bosonic canonical bath: hierarchical equations of motion approach.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

The final residue-corrected hierarchical equations of motion can be used practically for the evaluation of arbitrary dissipative quantum systems, and the corresponding continued-fraction Green's functions formalism for quantum dissipation is presented.

Exact quantum dissipative dynamics under external time-dependent driving fields

- Physics
- 2009

An exact and nonperturbative quantum master equation can be constructed via the calculus on the path integral. It results in hierarchical equations of motion for the reduced density operator.…

Time-dependent density functional theory for open quantum systems with unitary propagation.

- Physics, MedicinePhysical review letters
- 2010

We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS)…

Dissipaton dynamics theory versus quantum master equations

- ChemistryChemical Physics
- 2018

Abstract In this review article we present first a comprehensive account on the recently developed the dissipaton-equation-of-motion (DEOM) theory. This is a statistical quasi-particle theory for…

Exact quantum master equation via the calculus on path integrals.

- Physics, MedicineThe Journal of chemical physics
- 2005

An exact quantum master equation formalism is constructed for the efficient evaluation of quantum non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of…

Quantum Dynamics in a Fluctuating Environment

- Mathematics, Computer ScienceEntropy
- 2019

The projection operator technique is used to derive the exact quantum master equations of a qubit system with both diagonal splitting and tunneling coupling when the environmental noise is subject to a random telegraph process and a Ornstein-Uhlenbeck process.

Quantum mechanics of dissipative systems.

- Physics, MedicineAnnual review of physical chemistry
- 2005

This review examines both theoretical and application aspects on various perturbative formulations, especially those that are exact up to second-order but nonequivalent in high-order system-bath coupling contributions.

Open quantum systems in Heisenberg picture

- Mathematics, Physics
- 2019

In the framework of Heisenberg picture, an alternative derivation of reduced density matrix of a driven quantum system interacting with its environment is presented. To illustrate the approach, the…

Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach.

- Physics, MedicineThe Journal of chemical physics
- 2008

The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.

Time-Local Quantum Master Equations and their Applications to Dissipative Dynamics and Molecular Wires

- Physics
- 2009

The dynamics in open quantum systems is often described by quantum master equations (QMEs). Here a certain class of these master equations, the socalled time-local or time-convolutionless QMEs, are…

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