Distribution of waiting times between superoperator quantum jumps in Lindblad dynamics

TL;DR

This paper develops a method to compute the distribution of waiting times between quantum jumps in open quantum systems, using superoperator formalism, and demonstrates it on a Fermi-system in equilibrium.

Contribution

It introduces a novel approach based on superfermion/superboson formalism to analyze waiting time distributions in Lindblad dynamics.

Findings

Derived a formula for waiting time distribution in Lindblad systems

Applied the method to a thermodynamic equilibrium Fermi-system

Provided insights into quantum jump timing in open systems

Abstract

Time-evolution of open, dissipative quantum system is a stochastic process that consists of a series of quantum jumps that take place at random times. Between quantum jumps quantum system idles for some time in a particular quantum state. Based on superfermion/superboson formalism and general Kossakowski- Lindblad master equation for an open quantum system we develop a method to compute distribution of waiting times between quantum jumps. We illustrate the use of the theory by computing waiting time distribution for model Fermi-system in thermodynamic equilibrium.