Classical-Quantum Hybrid Models

Daniel R. Terno

doi:10.1016/B978-0-323-95703-8.00105-1

Classical-Quantum Hybrid Models

^*Corresponding author for this work

School of Mathematical and Physical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Entry for encyclopedia/dictionary/reference book › peer-review

Abstract

Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the motivation for such models, outline the requirements they must satisfy, and provide explanations for their development. Then we review various popular non-relativistic schemes and their associated limitations, with a particular emphasis on reversible dynamics.

Original language	English
Title of host publication	Encyclopedia of Mathematical Physics. Volume 2
Subtitle of host publication	Quantum Mechanics, Quantization & Quantum Computation
Editors	Robert Bruce Mann, Steven Rayan
Place of Publication	Cambridge MA
Publisher	Academic Press
Pages	57-72
Number of pages	16
Edition	2nd
ISBN (Electronic)	9780323957069
ISBN (Print)	9780323957038
DOIs	https://doi.org/10.1016/B978-0-323-95703-8.00105-1
Publication status	Published - 2025

Keywords

Classical limit
Hybrid mechanics
Koopman-von Neumann equation
Lindblad operators
Master equation
Mean-field theory
Moyal bracket
Phase space
Poisson-Lie algebra
Wigner transformation

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10.1016/B978-0-323-95703-8.00105-1

Cite this

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title = "Classical-Quantum Hybrid Models",

abstract = "Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the motivation for such models, outline the requirements they must satisfy, and provide explanations for their development. Then we review various popular non-relativistic schemes and their associated limitations, with a particular emphasis on reversible dynamics.",

keywords = "Classical limit, Hybrid mechanics, Koopman-von Neumann equation, Lindblad operators, Master equation, Mean-field theory, Moyal bracket, Phase space, Poisson-Lie algebra, Wigner transformation",

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Classical-Quantum Hybrid Models. / Terno, Daniel R.
Encyclopedia of Mathematical Physics. Volume 2: Quantum Mechanics, Quantization & Quantum Computation. ed. / Robert Bruce Mann; Steven Rayan. 2nd. ed. Cambridge MA: Academic Press, 2025. p. 57-72.

Research output: Chapter in Book/Report/Conference proceeding › Entry for encyclopedia/dictionary/reference book › peer-review

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PY - 2025

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AB - Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the motivation for such models, outline the requirements they must satisfy, and provide explanations for their development. Then we review various popular non-relativistic schemes and their associated limitations, with a particular emphasis on reversible dynamics.

KW - Classical limit

KW - Hybrid mechanics

KW - Koopman-von Neumann equation

KW - Lindblad operators

KW - Master equation

KW - Mean-field theory

KW - Moyal bracket

KW - Phase space

KW - Poisson-Lie algebra

KW - Wigner transformation

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BT - Encyclopedia of Mathematical Physics. Volume 2

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A2 - Rayan, Steven

PB - Academic Press

CY - Cambridge MA

ER -

Classical-Quantum Hybrid Models

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Keywords

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