Coherent states for Landau levels: algebraic and thermodynamical properties

TL;DR

This paper constructs and analyzes Barut-Girardello coherent states for charged particles in a magnetic field with a harmonic potential, exploring their algebraic structure and thermodynamical properties.

Contribution

It introduces a novel application of su(1, 1) algebra to Landau levels and develops a coherent state framework combined with thermodynamical analysis.

Findings

Construction of Barut-Girardello coherent states for the system

Analysis of the thermodynamical properties of the quantum gas

Application of Berezin-Klauder-Toeplitz quantization to the system

Abstract

This work describes coherent states for a physical system governed by a Hamiltonian operator, in two dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential. The underlying su(1, 1) Lie algebra and Barut-Girardello coherent states are constructed and discussed. Then, the Berezin - Klauder - Toeplitz quantization, also known as coherent state (or anti-Wick) quantization, is discussed. The thermodynamics of such a quantum gas system is elaborated and analyzed.