In order to construct time-dependent pseudo-bosonic coherent states, first, we extend the non-Hermitian integrals of motion method to cases where the quantum systems are described by time-dependent non-Hermitian Hamiltonians; second, we introduce a pseudo-bosonic annihilation operator defined as a time-dependent non-Hermitian linear invariant. The pseudo-bosons operators are a pseudo-Hermitian extension of usual boson operators. In fact, they are obtained from the modification of usual boson commutation relations where the annihilation and creation operators are related to their adjoint operators via the bounded Hermitian invertible operator or metric operator. Thus, the pseudo-bosonic coherent states are just obtained as eigenstates of the pseudo-bosonic annihilation operator. As an illustration, we study the time-dependent non-Hermitian Swanson Hamiltonian and we compare the obtained results with those in the literature (Swanson model but time-independent).
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October 2020
Research Article|
October 16 2020
Time-dependent pseudo-bosonic coherent states
Naima Mana
;
Naima Mana
a)
Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas Sétif 1
, Sétif 19000, Algeria
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Omar Zaidi;
Omar Zaidi
b)
Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas Sétif 1
, Sétif 19000, Algeria
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Mustapha Maamache
Mustapha Maamache
c)
Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas Sétif 1
, Sétif 19000, Algeria
c)Author to whom correspondence should be addressed: maamache@univ-setif.dz
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a)
E-mail: na3ima_mn@hotmail.fr
b)
E-mail: zaidiomar32@yahoo.com
c)Author to whom correspondence should be addressed: maamache@univ-setif.dz
J. Math. Phys. 61, 102103 (2020)
Article history
Received:
May 14 2020
Accepted:
September 26 2020
Citation
Naima Mana, Omar Zaidi, Mustapha Maamache; Time-dependent pseudo-bosonic coherent states. J. Math. Phys. 1 October 2020; 61 (10): 102103. https://doi.org/10.1063/5.0013723
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