Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons

TL;DR

This paper extends the theory of pseudo-bosons to two-dimensional systems, applying it to generalized Landau levels and a damped harmonic oscillator, and explores their coherent states and mathematical properties.

Contribution

It introduces a two-dimensional framework for pseudo-bosons and applies it to generalized Landau levels and damped oscillators, expanding the theoretical understanding.

Findings

Generalized Landau levels analyzed with pseudo-bosons

Coherent states and resolution of identity derived

Application to classical damped harmonic oscillator

Abstract

In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.