Nonlinear quantum mechanics in a q-deformed Hilbert space

Pradip Das

Marco Del Seta, Gianpiero Cattaneo

Isiaka Aremua, Mahouton Norbert Hounkonnou

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.

Jian-zu Zhang

G Vinod

Isiaka Aremua, Mahouton Norbert Hounkonnou, Ezinvi Baloïtcha

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.