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Quantum work statistics in regular and classical-chaotic dynamical billiard systems
Sebastian Rosmej1, Mattes Heerwagen1
1Carl von Ossietzky Universität Oldenburg, Institut für Physik, D-26111 Oldenburg, Germany.
Physical Review. E
|June 16, 2022
Summary
This study compares classical and quantum descriptions of nanoscopic systems using two-dimensional billiard models. It analyzes work distribution and angular momentum, revealing interesting quantum-classical connections.
Area of Science:
- Thermodynamics of nanoscopic systems
- Quantum mechanics
- Classical mechanics
Background:
- The relationship between classical and quantum descriptions is crucial for nanoscopic systems.
- Defining mechanical work in small quantum systems remains a challenge.
Purpose of the Study:
- To scrutinize the correspondence between classical and quantum mechanics in nanoscopic systems.
- To analyze work distribution and angular momentum in two-dimensional billiard systems.
- To investigate the definition of mechanical work in quantum systems.
Main Methods:
- Studied two two-dimensional billiard systems in both classical and quantum settings.
- Calculated classical conditional probability density and quantum mechanical transition probability.
- Analyzed work distribution, zero work probability, and zero angular momentum difference.
Main Results:
- Derived analytical formulas for both systems using connections to an exactly solvable system.
- Obtained numerical results in the quantum case showing interesting relations to the classical case.
- Investigated the controversial definition of mechanical work in small quantum systems.
Conclusions:
- The study provides insights into the classical-quantum correspondence in nanoscopic thermodynamics.
- Findings highlight the importance of statistical analysis for understanding quantum systems.
- Results contribute to the ongoing discussion on mechanical work in quantum thermodynamics.
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