Browsing by Author "Ananya Ghatak"

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A black potential for spin less particles
(Elsevier B.V., 2015) Ananya Ghatak; Mohammad Hasan; Bhabani Prasad Mandal
We consider the most general non-Hermitian Hulthen potential to study the scattering of spin-less relativistic particles. The conditions for CC, SS and CPA are obtained analytically for this potential. We show that almost total absorption occurs for entire range of incidence energy for certain parameter ranges of the potential and hence term this as 'black potential'. Time reversed of the same potential shows perfect emission for the entire range of particle energy. We also present the classical analog of this potential in terms of waveguide cross section. © 2015 Elsevier B.V. All rights reserved.
Comparison of different approaches of finding the positive definite metric in pseudo-Hermitian theories
(2013) Ananya Ghatak; Bhabani Prasad Mandal
To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models. © 2013 Chinese Physical Society and IOP Publishing Ltd.
Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system
(2014) Mohammad Hasan; Ananya Ghatak; Bhabani Prasad Mandal
We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system. © 2014 Elsevier Inc.
Entangled quantum state discrimination using a pseudo-Hermitian system
(2012) Ananya Ghatak; Bhabani Prasad Mandal
We demonstrate how to discriminate two non-orthogonal, entangled quantum states which are slightly different from each other by using a pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian system fully consistent with quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such an evolution ceases at exceptional points of the pseudo-Hermitian system. © 2012 IOP Publishing Ltd.
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.
Spectral singularity and non-Hermitian PT-symmetric extension of an AN 1-type Calogero model without confining potential
(2012) Bhabani Prasad Mandal; Ananya Ghatak
We consider non-Hermitian PT-symmetric deformation of an AN 1-type Calogero model without confining potential to investigate the possible existence of spectral singularity. By considering the Wronskian between asymptotic incoming and outgoing scattering state wavefunctions, we found that there exists no spectral singularity in this model. We further explicitly show that the transmission coefficient vanishes and the reflection coefficient becomes unity for all values of the energy in such a momentum-dependent non-Hermitian PT-symmetric model. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to Quantum physics with non-Hermitian operators. © 2012 IOP Publishing Ltd.
Spectral singularity and reflectionlessness in non-Hermitian (complex) Ginocchio potential
(2012) Ananya Ghatak; Joseph Amal Nathan; Bhabani Prasad Mandal; Zafar Ahmed
Recently, interest in scattering from complex non-Hermitian potentials has been renewed both theoretically and experimentally. When a potential becomes complex, several new features arise which may not be predicted. In this regard, we study the non-Hermitian version of the exactly solvable, versatile Ginocchio potential. We find that when it is non-Hermitian and non-absorptive there exists, at most, one spectral singularity (SS). The well-known reflectionlessness of this potential gives way to deep minima in reflectivity. We find the co-existence of an SS with deep oscillations in reflectivity. Remarkably, the complex PT-symmetric version of this potential does not entail any SS. In this case, the reflectionlessness at discrete energies persists with the handedness of reflectivity and non-unitarity. In the new parlance this would be called the invisibility of an optical potential but in this case, uniquely, it is from both sides, left and right. © 2012 IOP Publishing Ltd.
Various scattering properties of a new PT-symmetric non-Hermitian potential
(2013) Ananya Ghatak; Raka Dona Ray Mandal; Bhabani Prasad Mandal
We complexify a 1-d potential V (x) = V0cosh 2μ{ tanh [ (x -μd) / d] + tanh (μ) } 2 which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ, d) becomes imaginary. For the case of μ → iμ, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from the left (or right) at certain discrete energies. The penetrating states in the other case (d → i d) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. © 2013 Elsevier Inc.