Non-Markovian quantum state diffusion: Perturbation approach

Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not guaranteed. In this paper, we provide a general class of time-local, perturbative and positivity-preserving non-Markovian master equations generated from stochastic Schrodinger equations, particularly quantum-state-diffusion equations. Our met...

We present a nonlinear stochastic Schroedinger equation for pure states describing non-Markovian diffusion of quantum trajectories. It provides an unravelling of the evolution of a quantum system coupled to a finite or infinite number of harmonic oscillators, without any approximation. Its power is illustrated by several examples, including measurement-like situations, dissipation, and quantum Brownian motion. In some examples, we treat the environment phenomenologically as a...

A long-standing open problem in non-Markovian quantum state diffusion (QSD) approach to open quantum systems is to establish the non-Markovian QSD equations for multiple qubit systems. In this paper, we settle this important question by explicitly constructing a set of exact time-local QSD equations for $N$-qubit systems. Our exact time-local (convolutionless) QSD equations have paved the way towards simulating quantum dynamics of many-body open systems interacting with a com...

We develop a systematic and efficient approach for numerically solving the non-Markovian quantum state diffusion equations for open quantum systems coupled to an environment up to arbitrary orders of noises or coupling strengths. As an important application, we consider a real-time simulation of a spin-boson model in a strong coupling regime that is difficult to deal with using conventional methods. We show that the non-Markovian stochastic Schr\"{o}dinger equation can be eff...

A general method is discussed to obtain Markovian master equations which describe the interaction with the environment in a microscopic and non-perturbative fashion. It is based on combining time-dependent scattering theory with the concept of continuous quantum measurements. The applications to the case of a Brownian point particle and to the case of a complex molecule, both in the presence of a gaseous environment, are outlined.

Perturbation theory (PT) is a powerful and commonly used tool in the investigation of closed quantum systems. In the context of open quantum systems, PT based on the Markovian quantum master equation is much less developed. The investigation of open systems mostly relies on exact diagonalization of the Liouville superoperator or quantum trajectories. In this approach, the system size is rather limited by current computational capabilities. Analogous to closed-system PT, we de...

A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation and quantum thermodynamics. In this paper,...

The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the influence of friction in the quantum realm is based on master equations which require, however, in one or the other aspect approximations. Here it is discussed under which conditions and limitations Markovian master equations can be derived from ex...

The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schr\"{o}dinger equation called time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov a...

We generalize the classical theory of Brownian motion so as to reckon with non-Markovian effects on both Klein-Kramers and Smoluchowski equations. For a free particle and a harmonic oscillator, it is shown that such non-Markovian effects account for the differentiability of the Brownian trajectories as well as the breakdown of the energy equipartition of statistical mechanics at short times in some physical situations. This non-Markovian approach is also extended to look at a...