A brief overview is given of recent developments and fresh ideas at the intersection of PT-and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). Within the framework of the resulting supersymmetric version of CPT-symmetric quantum mechanics we study the consequences of the assumption that the "charge" operator C is represented in a, differential-operator form of the second or higher order. Besides the freedom allowed by the Hermiticity constraint for the operator CP, encouraging results are obtained in the second-order case. In particular, the integrability of intertwining relations proves to match the closure of our nonlinear (viz., polynomial) SUSY algebra. In a particular illustration, our form of CPT-symmetric SUSY QM leads to a new class of non-Hermitian polynomial oscillators with real spectrum which turn out to be PT-asymmetric. © World Scientific Publishing Company.

B BAGCHI

A BANERJEE

E CALICETI

F CANNATA

C QUESNE

M ZNOJIL

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

International Journal of Modern Physics A

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 [formula omitted] are naturally embedded. Different representations of the charge operator are considered that lead to new mass-deformed superpotentials [formula omitted] which are inherently [formula omitted]-symmetric. The qualitative spectral behavior of Hm is studied and several interesting consequences are noted. © 2013, American Institute of Physics. All rights reserved.

Journal of Mathematical Physics

[formula omitted]-conserved effective mass Hamiltonians through first and higher order charge operator [formula omitted] in a supersymmetric framework

This paper examines the features of a generalized position-dependent mass Hamiltonian H-m 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 W-m(x) which are inherently PT-symmetric. The qualitative spectral behavior of H-m is studied and several interesting consequences are noted. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4792472]

CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework

We examine a generalized PT-symmetric quartic anharmonic oscillator model to determine the various physical variables perturbatively in powers of a small quantity ε. We make use of the Bender-Dunne operator basis elements and exploit the properties of the totally symmetric operator Tm,n. © World Scientific Publishing Company.

Modern Physics Letters A

A perturbative treatment of a generalized PT-symmetric quartic anharmonic oscillator

Working within the framework of parity-time-symmetric quantum mechanics, we look into the possibility of entanglement generation and demonstrate that the feature of non-violation of no-signaling principle may hold for the simplest nontrivial case of bipartite systems. Basically, our arguments are based on the computation of the reduced density matrix of one party to justify that the entropy of the other does not change. © 2020 World Scientific Publishing Company.

Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics

Series of exactly solvable non-trivial complex potentials (possessing real spectra) are generated by applying the Darboux transformation to the excited eigenstates of a non-Hermitian potential V(x). This method yields an infinite number of non-trivial partner potentials, defined over the whole real line, whose spectra are nearly exactly identical to the original potential.

Czechoslovak Journal of Physics

Generation of exactly solvable non-Hermitian potentials with real energies

We discuss certain features of pseudo-Hermiticity and weak pseudo-Hermiticity conditions and point out that, contrary to a recent claim, there is no inconsistency if the correct orthogonality condition is used for the class of pseudo-Hermitian, PT symmetric Hamiltonians of the type Hβ = [p + iβv(x)]2/2m + V (x). © 2002 Elsevier Science B.V. All rights reserved.

Physics Letters, Section A: General, Atomic and Solid State Physics

Pseudo-Hermiticity, weak pseudo-Hermiticity and Î·-orthogonality condition

The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength Z lies below the critical value Z 0 (c) where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY partner potentials, depicting an unbroken SUSY situation and reducing to the family of sec 2-like potentials in the Z → 0 limit. For Z above Z 0 (c), there is a rich diversity of SUSY hierarchies, including some with PT-symmetry breaking and some with partial PT-symmetry restoration.

PT-symmetric square well and the associated SUSY hierarchies

A new model of supersymmetry between bosons and fermions is proposed. Its representation space is spanned by states with PT symmetry and real energies but the inter-related partner Hamiltonians themselves remain complex and non-Hermitian. The formalism admits vanishing Witten index. (C) 2000 Elsevier Science B.V.

Journal	International Journal of Modern Physics A
Publisher	WORLD SCIENTIFIC PUBL CO PTE LTD
ISSN	0217-751X
Open Access	Yes