Introduction to the theory of open quantum systems

Abstract

This manuscript is an edited and refined version of the lecture script for a one-semester graduate course given originally at the PhD school in the Institute of Physics of Polish Academy of Sciences in the Spring/Summer semester of 2022. The course expects from the student only a basic knowledge on graduate-level quantum mechanics. The script itself is largely self-contained and could be used as a textbook on the topic of open quantum systems. The program of this course is based on a novel approach to the description of the open system dynamics: It is showed how the environmental degrees of freedom coupled to the system can be represented by a multi-component quasi-stochastic process. Using this representation one constructs the super-quasi-cumulant (or super-qumulant) expansion for the system's dynamical map -- a parametrization that naturally lends itself for the development of a robust and practical perturbation theory. Thus, even an experienced researcher might find this manuscript of some interest.

136 pages; Submission to SciPost Physics Lecture Notes

References in corpus (4)

• Markovian Master Equations: A Critical Study
• A Brief History of the GKLS Equation
• Measuring trajectories of environmental noise
• Dynamical maps beyond Markovian regime

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• Double or nothing: a Kolmogorov extension theorem for multitime (bi)probabilities in quantum mechanics
• ${}^{164}\mathrm{Pb}$: A possible heaviest $N=Z$ doubly magic nucleus
• A perturbation theory for multi-time correlation functions in open quantum systems
• Electron dynamics induced by quantum cat-state light
• Phenomenological quantum mechanics: I. Phenomenology of quantum observables