On nonlinear coherent states properties for electron-phonon dynamics

TL;DR

This paper constructs and analyzes nonlinear coherent states within a deformed algebra framework, exploring their mathematical properties, phase space quantization, and quantum optical applications in condensed matter physics.

Contribution

It introduces a dual pair of nonlinear coherent states for a deformed algebra model and studies their properties, including reproducing kernels and phase space quantization.

Findings

Reproducing kernel properties are established for the NCS Hilbert space.

A $q$-deformed coherent states example illustrates the quantization process.

Quantum optical properties of the NCS are analyzed.

Abstract

This work addresses a construction of a dual pair of nonlinear coherent states (NCS) in the context of changes of bases in the underlying Hilbert space for a model pertaining to the condensed matter physics, which obeys a $f$-deformed Heisenberg algebra. The existence and properties of reproducing kernel in the NCS Hilbert space are studied and discussed; the probability density and its dynamics in the basis of constructed coherent states are provided. A Glauber-Sudarshan $P$-representation of the density matrix and relevant issues related to the reproducing kernel properties are presented. Moreover, a NCS quantization of classical phase space observables is performed and illustrated in a concrete example of $q$-deformed coherent states. Finally, an exposition of quantum optical properties is given.