$\mathcal {CPT}$
                CPT
          -conserved effective mass Hamiltonians through first and higher order charge operator $\mathcal {C}$C in a supersymmetric framework

Bagchi, B.; Banerjee, Abhijit; Ganguly, Asish

doi:10.1063/1.4792472

Journal of Mathematical Physics

2013

DOI: 10.1063/1.4792472

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$\mathcal {CPT}$ CPT -conserved effective mass Hamiltonians through first and higher order charge operator $\mathcal {C}$C in a supersymmetric framework

B. Bagchi

Abhijit Banerjee

Asish Ganguly

Abstract: This paper examines the features of a generalized position-dependent mass Hamiltonian Hm in a supersymmetric framework in which the constraints of pseudo-Hermiticity and CPT are naturally embedded. Different representations of the charge operator are considered that lead to new mass-deformed superpotentials Wm(x) which are inherently PT-symmetric. The qualitative spectral behavior of Hm is studied and several interesting consequences are noted.

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Cited by 4 publications

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Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform

Ganguly

Das

2014

Journal of Mathematical Physics

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We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1 + 1) dimension through Lax pair formulation, one being the effective mass Schrödinger operator and the other being the time-evolution of wave functions. We obtain an infinite number of conserved quantities for the generated nonlinear equation and explicitly show that the new generalized KdV equation is an integrable system. Inverse scattering transform method is applied to obtain general solution of the nonlinear equation, and then N-soliton solution is derived for reflectionless potentials. Finally, a special choice has been made for the variable mass function to get massdeformed soliton solution. The influence of position and time-dependence of mass and also of the different representations of kinetic energy operator on the nature of such solitons is investigated in detail. The remarkable features of such solitons are demonstrated in several interesting figures and are contrasted with the conventional KdV-soliton associated with constant-mass quantum model. C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4900895]In this equation T EM (x) is the EM kinetic energy operator and ψ(x) is known as envelope wavefunction. Due to the non-commutativity of momentum operator p ≡ − i ∂ x and the effective mass operator m(x), an infinite number of representation is possible for the kinetic energy operator. It is well-known that a hermitian form is induced by a general two-parameter family 37(1.2)Note that the form (1.2) is not the most general form. Other non-hermitian forms exist. However, to the best of our knowledge, it is the general form among hermitian family. It has to be mentioned that although different possible representations are covered in (1.2), some special forms attract much a) Electronic addresses:

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Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform

Ganguly

Das

2014

Journal of Mathematical Physics

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Unitarity corridors to exceptional points

Znojil

2019

Phys. Rev. A

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Phenomenological quantum Hamiltonians H (N ) (λ) = J (N ) + λ V (N ) (λ) representing a general real N 2 −parametric perturbation of an exceptional-point-related unperturbed Jordan-block Hamiltonian J (N ) are considered. Tractable as non-Hermitian (in a preselected, unphysical Hilbert space) as well as, simultaneously, Hermitian (in another, "physical" Hilbert space) these matrices may represent a unitary, closed quantum system if and only if the spectrum is real. At small λ we show that the parameters are then confined to a "stability corridor" S of the λ → 0 access to the extreme dynamical exceptional-point regime. The corridors are N−dependent and narrow: They are formed by a non-empty subset of unitarity-compatible multiscale perturbations such that λ V (N ) j+k,j (λ) = O(λ (k+1)/2 ) at k = 1, 2, . . . , N − 1 and all j.

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Problem of the coexistence of several non-Hermitian observables in PT -symmetric quantum mechanics

et al. 2017

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During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators Λ (with real spectra) which are manifestly non-Hermitian in a preselected "friendly" Hilbert space H (F ) . The consistency of these models is known to require an upgrade of the inner product, i.e., mathematically speaking, a transition H (F ) → H (S) to another, "standard" Hilbert space.We prove that whenever we are given more than one candidate for an observable (i.e., say, two operators Λ 0 and Λ 1 ) in advance, such an upgrade need not exist in general.

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$\mathcal {CPT}$ CPT -conserved effective mass Hamiltonians through first and higher order charge operator $\mathcal {C}$C in a supersymmetric framework

Cited by 4 publications

References 47 publications

Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform

Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform

Unitarity corridors to exceptional points

Problem of the coexistence of several non-Hermitian observables in PT -symmetric quantum mechanics

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