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Updated: Sep 11, 2025
09:23
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
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Ideal gas law for a quantum particle.
Alejandro M F Rivas1, Eduardo G Vergini1, Leonardo Ermann1
1Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Comisión Nacional de Energía Atómica (CNEA), Departamento de Física Teórica, GIyA, Libertador 8259 (C1429BNP), CABA, Argentina and , Godoy Cruz 2290 (C1425FQB), CABA, Argentina.
Physical Review. E
|August 19, 2025
Summary
This study explores how classical thermodynamics, like the ideal gas law (IGL), emerges from quantum mechanics for a single particle in a cavity. Quantum properties influence IGL validity, especially in non-uniform systems.
Area of Science:
- Quantum mechanics
- Thermodynamics
- Statistical physics
Background:
- Classical thermodynamic laws are fundamental but their quantum origins remain a key question in physics.
- Understanding the emergence of macroscopic laws from microscopic quantum behavior is crucial.
Purpose of the Study:
- To investigate the validity of the ideal gas law (IGL) for a single quantum particle in a 2D cavity.
- To explore how quantum effects and system geometry influence thermodynamic properties.
Main Methods:
- Interpreting quantum wave functions as probability densities.
- Applying the energy equipartition principle to define quantum temperature.
- Utilizing two distinct definitions for mean pressure, including radiation pressure and a quasi-orthogonality relation for billiard eigenstates.
- Analyzing systems with regular (circular, rectangular billiards) and chaotic (Bunimovich stadium) dynamics.
Main Results:
- The IGL holds exactly for isotropic systems (circular billiard) using the radiation pressure definition.
- Anisotropic systems show quantum eigenfunctions conforming to the IGL on average, with deviations.
- Deviations from IGL decrease with chaotic dynamics and coherent states, aligning with the eigenstate thermalization hypothesis (ETH).
- A second pressure definition shows good agreement with the IGL.
Conclusions:
- The ideal gas law's validity is influenced by quantum mechanics, system geometry, and dynamics.
- Quantum effects can lead to deviations from classical laws, particularly in anisotropic systems.
- The study provides insights into the quantum-classical transition and the foundations of thermodynamics.
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