Kinetic Energy of a Trapped Fermi Gas at Finite Temperature

Area of Science:

• Quantum mechanics
• Statistical physics

Background:

• Studying the statistical properties of quantum systems is crucial for understanding their behavior.
• Fermions in a harmonic trap are a fundamental model in quantum many-body physics.

Purpose of the Study:

• To derive an exact solution for the kinetic energy distribution of N noninteracting fermions in a 1D harmonic trap at finite temperature.
• To identify and characterize the quantum and thermal regimes governing the energy statistics.

Main Methods:

• Utilizing a non-trivial mapping to an integrable Calogero-Moser-Sutherland model.
• Analyzing the full distribution of kinetic energy at any temperature and particle number.

Main Results:

• An exact solution for the kinetic energy distribution was obtained.
• Two distinct regimes were identified: a quantum regime (T~ℏω) dominated by quantum fluctuations and a thermal regime (T~Nℏω) dominated by thermal fluctuations.
• The crossover between these regimes was characterized by examining the mean, variance, and large deviation function.

Conclusions:

• The study provides a comprehensive understanding of kinetic energy statistics in a 1D fermionic system.
• The findings highlight the interplay between quantum and thermal fluctuations in determining system properties.
• The exact solution offers a valuable tool for theoretical and experimental investigations.