A stochastic approach to open quantum systems

Abstract

Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in contact with a somehow bigger system, an environment, that is considered in thermal equilibrium. Any small fluctuation of the environment has some random effect on the system. In Physics, stochastic methods have been applied to the investigation of phase transitions, thermal and electrical noise, thermal relaxation, quantum information, Brownian motion etc. In this review, we will focus on the so-called stochastic Schrödinger equation. This is useful as a starting point to investigate the dynamics of open quantum systems capable of exchanging energy and momentum with an external environment. We discuss in some details the general derivation of a stochastic Schrödinger equation and some of its recent applications to spin thermal transport, thermal relaxation, and Bose-Einstein condensation. We thoroughly discuss the advantages of this formalism with respect to the more common approach in terms of the reduced density matrix. The applications discussed here constitute only a few examples of a much wider range of applicability.

43 pages, 9 figures, iopart style, published in Journal of Physics: Condensed Matter

References in corpus (13)

• Spontaneous vortices in the formation of Bose-Einstein condensates
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Modeling heat transport through completely positive maps
• Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems
• On the "Causality Paradox" of Time-Dependent Density Functional Theory
• Stochastic Time-Dependent Current-Density-Functional Theory
• Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
• Portable implementation of a quantum thermal bath for molecular dynamics simulations
• Global fixed point proof of time-dependent density-functional theory
• Stochastic time-dependent current-density functional theory: a functional theory of open quantum systems
• Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
• Dynamical thermalization and vortex formation in stirred 2D Bose-Einstein condensates

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