Journal of Nonlinear Mathematical Physics

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Volume 21, Issue 1, February 2014, Pages 89 - 119

On nonlinear coherent states properties for electron-phonon dynamics

Authors
Isiaka Aremua†, Mahouton Norbert Hounkonnou‡, Ezinvi Baloïtcha*
University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), 072 B.P. 50 Cotonou, Republic of Benin
Received 12 September 2013, Accepted 2 December 2013, Available Online 6 January 2021.
DOI
10.1080/14029251.2014.894723How to use a DOI?
Keywords
Deformed Heisenberg algebra; Electron-phonon dynamics; Coherent states; Coherent state quantization
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 an electron-phonon model in the condensed matter physics, obeying 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.

Copyright
© 2014 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
21 - 1
Pages
89 - 119
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2014.894723How to use a DOI?
Copyright
© 2014 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Isiaka Aremua
AU  - Mahouton Norbert Hounkonnou
AU  - Ezinvi Baloïtcha
PY  - 2021
DA  - 2021/01/06
TI  - On nonlinear coherent states properties for electron-phonon dynamics
JO  - Journal of Nonlinear Mathematical Physics
SP  - 89
EP  - 119
VL  - 21
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2014.894723
DO  - 10.1080/14029251.2014.894723
ID  - Aremua2021
ER  -