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Dissipative properties of quantum systems.

A P Grecos¹, I Prigogine

¹Faculté des Sciences, Université Libre de Brusselles, 1050 Brussels-Belgium.

Proceedings of the National Academy of Sciences of the United States of America

|June 1, 1972

Summary

We explore quantum system dissipation using kinetic theory. A simplified model reveals how collision operators dictate system invariants and lead to ergodic behavior in large quantum systems.

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Area of Science:

Quantum Mechanics
Statistical Mechanics
Kinetic Theory

Background:

Dissipative properties of large quantum systems are crucial for understanding their behavior.
Kinetic theory provides a framework for analyzing many-body quantum systems.
Collision operators play a key role in determining system dynamics and invariants.

Purpose of the Study:

To investigate the dissipative properties of large quantum systems using kinetic theory.
To analyze the restrictions imposed by nontrivial collision operators on collisional invariants.
To examine the ergodic behavior of quantum systems with small physical parameters.

Main Methods:

Utilized kinetic theory to model dissipative properties.
Employed a simplified quantum system model (Friedrichs model in the large volume limit).
Directly calculated the collision operator and constants of motion.

Main Results:

Demonstrated that nontrivial collision operators restrict collisional invariants.
Showcased the special role of Hamiltonian-dependent invariants due to nonvanishing collision operators.
Obtained ergodic behavior for a class of observables.

Conclusions:

The study provides a kinetic theory perspective on quantum system dissipation.
The findings highlight the connection between collision operators, invariants, and ergodic behavior.
The reformulation of the ergodic problem offers a new approach to studying large quantum systems.

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