Browsing by Author "Brijesh Kumar Mourya"

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Green’s function of a general PT-symmetric non-Hermitian non-central potential
(Springer Science and Business Media, LLC, 2016) Brijesh Kumar Mourya; Bhabani Prasad Mandal
We study the path integral solution of a system of particle moving in certain class of PT symmetric non-Hermitian and non-central potential. The Hamiltonian of the system is converted to a separable Hamiltonian of Liouville type in parabolic coordinates and is further mapped into a Hamiltonian corresponding to two 2-dimensional simple harmonic oscillators (SHOs). Thus the explicit Green’s functions for a general non-central PT symmetric non hermitian potential are calculated in terms of that of 2d SHOs. The entire spectrum for this three dimensional system is shown to be always real leading to the fact that the system remains in unbroken PT phase all the time. © Springer International Publishing Switzerland 2016.
PT phase transition in higher-dimensional quantum systems
(Elsevier B.V., 2013) Bhabani Prasad Mandal; Brijesh Kumar Mourya; Rajesh Kumar Yadav
We consider a 2d anisotropic SHO with ixy interaction and a 3d SHO in an imaginary magnetic field with μ→l.B→ interaction to study the PT phase transition analytically in higher dimension. Unbroken PT symmetry in the first case is complementary to the rotational symmetry of the original Hermitian system. PT phase transition ceases to occur the moment the 2d oscillator becomes isotropic. Transverse magnetic field in the other system introduces the anisotropy in the system and the system undergoes PT phase transition depending on the strength of the magnetic field and frequency of the oscillator. All these results in higher dimensions are based on exact analytical calculations. © 2013 Elsevier B.V. All rights reserved.
QES solutions of a two-dimensional system with quadratic nonlinearities
(Springer Science and Business Media Deutschland GmbH, 2020) Bhabani Prasad Mandal; Brijesh Kumar Mourya; Aman Kumar Singh
We consider a one-parameter family of a PT symmetric two-dimensional system with quadratic nonlinearities. Such systems are shown to perform periodic oscillations due to existing centers. We describe this system by constructing a non-Hermitian Hamiltonian of a particle with position-dependent mass. We further construct a canonical transformation which maps this position-dependent mass system to a QES system. First few QES levels are calculated explicitly by using Bender–Dunne polynomial method. © 2020, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
Reciprocity in Parity Violating Non-Hermitian Systems
(Springer New York LLC, 2015) Ananya Ghatak; Brijesh Kumar Mourya; Raka Dona Ray Mandal; Bhabani Prasad Mandal
Reciprocity is shown so far only when the scattering potential is either real or parity symmetric complex. We extend this result for parity violating complex potential by considering several explicit examples: (i) we show reciprocity for a PT symmetric (hence parity violating) complex potential which admits penetrating state solutions analytically for all possible values of incidence energy and (ii) reciprocity is shown to hold at certain discrete energies for two other parity violating complex potentials. © 2014, Springer Science+Business Media New York.