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Quantum-Classical Hybrid Systems and Ehrenfest's Theorem.

Alessandro Sergi^1,2, Daniele Lamberto¹, Agostino Migliore³

¹Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.

Entropy (Basel, Switzerland)

|May 16, 2023

Summary

This summary is machine-generated.

We generalized Ehrenfest's theorem for bipartite quantum systems, enabling the study of quantum-classical hybrids. This work provides a new method for analyzing quantum-classical systems and developing numerical simulations.

Keywords:

Ehrenfest’s theorem open quantum systems quantum mechanics in phase space quantum–classical dynamics

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Area of Science:

Quantum mechanics
Theoretical physics
Quantum-classical systems

Background:

A theory consistent with observations must describe both quantum and classical systems (quantum-classical hybrids).
Orthodox measurement interpretations necessitate transient quantum-classical hybrids.
Ehrenfest's theorem provides a basic link between quantum and classical mechanics.

Purpose of the Study:

Generalize Ehrenfest's theorem to bipartite quantum systems.
Develop a formalism to study quantum-classical hybrids.
Derive the form of the Ehrenfest theorem for quantum-classical hybrids.

Main Methods:

Operator-valued Wigner functions
Quantum-classical brackets
Generalization of Ehrenfest's theorem

Main Results:

The time variation of average energy in bipartite systems equals the average symmetrized quantum dissipated power.
This holds true for both purely quantum and quantum-classical cases.
A derived form of Ehrenfest's theorem for quantum-classical hybrids.

Conclusions:

Theoretical results are useful for analyzing quantum-classical hybrids.
The findings aid in developing self-consistent numerical algorithms for Ehrenfest-type simulations.
This work advances the understanding of quantum-classical interactions.