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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.

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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.