Density operator approach for Landau problem quantum Hamiltonians

TL;DR

This paper develops a density operator framework for quantum Hamiltonians in Landau problems, analyzing thermodynamics and entropy in magnetic and noncommutative settings, including fractional quantum Hall effects.

Contribution

It introduces a density operator approach for Landau Hamiltonians, incorporating noncommutative geometry and fractional quantum Hall models, with a focus on thermodynamic and informational measures.

Findings

Derived the Q-Husimi distribution for these models

Calculated Wehrl entropy in the Landau and fractional quantum Hall contexts

Established the role of coherent states in thermodynamic analysis

Abstract

In this work, the definition of the density operator on quantum states in Hilbert spaces and some of its aspects relevant in thermodynamics and information-theoretical entropy calculations are given. In this framework, a physical model describing an electron in a magnetic field is investigated. The so-called exotic Landau problem in noncommutative plane is also considered. Then, a model related to the fractional quantum Hall effect is revisited. Thanks to the completeness relations verified by the coherent states (CS) in these models, the thermodynamics is discussed by using the diagonal $P$-representation of thedensity operator. Specifically, the Q-Husimi distribution and the Wehrl entropy are determined.