Related papers: Stochastic Processes: From Classical to Quantum

Stochastic Processes: From Classical to Quantum

URL: http://arxiv.org/abs/2407.04005v1
Date: Thu, 4 Jul 2024 15:26:35 GMT
Title: Stochastic Processes: From Classical to Quantum
Authors: Soon Hoe Lim,
Abstract summary: We start with some reminders from the theory of classical processes. We then provide a brief overview of quantum mechanics and quantum field theory. We introduce quantum processes on a boson Fock space and their calculus.
Score: 7.034466417392574
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic processes. We then provide a brief overview of quantum mechanics and quantum field theory, from the viewpoint of quantum probability and adopting the language of Hudson and Parthasarathy. We introduce quantum stochastic processes on a boson Fock space and their calculus. Whenever possible, we make connections with the relevant concepts in classical probability theory. As an application of the theory, we introduce the theory of open quantum systems, with emphasis on the physics and modeling aspects of these systems.

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