Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/0203252

Re-establishing supersymmetry between harmonic oscillators in $D \neq 1$ dimensions

Miloslav Znojil

Published Mar 27, 2002• 0 citations
arXivHTMLPDF

Abstract

Using a PT symmetric regularization technique we reminad the reader that and how (a) the SUSY is re-established between the two shifted harmonic oscillator potentials $ V(q)=q^2+{G}/{q^2}+ const$ and (b) many non-equivalent Hermitian and non-Hermitian (PT symmetric) systems may often be studied in parallel (with a schematic solvable illustrative example added).

DOI
10.48550/arxiv.hep-th/0203252

Related papers

Non-Hermitian supersymmetry and singular, 𝒫𝒯-symmetrized oscillators

Miloslav Znojil

Hermitian supersymmetric partnership between singular potentials V ( q ) = q 2 + G / q 2 breaks down and can only be restored on certain ad hoc subspaces (Das A and Pernice S 1999 Nucl. Phys. B 561 357). We show that within extended, -symmetric quantum mechanics, the supersymmetry between singular oscillators can be completely re-established in a way which is continuous near G = 0 and leads to a new form of the bosonic creation and annihilation operators.

arXiv:hep-th/0201056•Journal of Physics A Mathematical and General•Feb 25, 2002•55 citations

SUSY transformations between diagonalizable and non-diagonalizable Hamiltonians

B. F. Samsonov

Recently (see quant-ph/0503040) an explicit example has been given of a PT-symmetric non-diagonalizable Hamiltonian. In this paper we show that such Hamiltonians appear as supersymmetric (SUSY) partners of Hermitian (hence diagonalizable) Hamiltonians and they can be turned back to diagonalizable forms by appropriate SUSY transformations.

arXiv:quant-ph/0503075•Journal of Physics A Mathematical and General•May 10, 2005•41 citations

The interplay of supersymmetry and PT symmetry in quantum mechanics: a case study for the Scarf II potential

GÉZA LÉVAI, Miloslav Znojil

Motivated by the duality of normalizable states and the presence of the quasi-parity quantum number q=+/-1 in PT symmetric (non-Hermitian) quantum mechanical potential models, the relation of PT symmetry and supersymmetry (SUSY) is studied. As an illustrative example the PT invariant version of the Scarf II potential is presented, and it is shown that the "bosonic" Hamiltonian has two different "fermionic" SUSY partner Hamiltonians (potentials) generated from the ground-state solutions with q=1 and q=-1. It is shown that the "fermionic" potentials cease to be PT invariant when the PT symmetry of the "bosonic" potential is spontaneously broken. A modified PT symmetry inspired SUSY construction is also discussed, in which the SUSY charge operators contain the antilinear operator T. It is shown that in this scheme the "fermionic" Hamitonians are just the complex conjugate of the original "fermionic" Hamiltonians, and thus possess the same energy eigenvalues.

arXiv:quant-ph/0206013•Jun 3, 2002•0 citations

Shape Invariant Potential and Semi-Unitary Transformations (SUT) for Supersymmetry Harmonic Oscillator in T 4-Space

P. S. Bisht, O. P. S. Negi

arXiv:hep-th/0608041•International Journal of Theoretical Physics•Oct 22, 2008•0 citations

Exactly solvable $\mathcal{PT}$ -symmetric models in two dimensions

Kaustubh S. Agarwal, Rajeev K. Pathak, Yogesh N. Joglekar

Non-Hermitian, PT -symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, PT potentials for a non-relativistic particle confined in a circular geometry. We show that the PT -symmetry threshold can be tuned by introducing a second gain-loss potential or its Hermitian counterpart. Our results explicitly demonstrate that PT breaking in two dimensions has a rich phase diagram, with multiple re-entrant PT -symmetric phases.

arXiv:1510.01014•Europhysics Letters (EPL)•Nov 1, 2015•12 citations

A non-Hermitian oscillator Hamiltonian and su(1, 1): a way towards generalizations

C. Quesne

The family of metric operators, constructed by Musumbu et al (2007 J. Phys. A: Math. Theor. 40 F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian PT-symmetric part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of generalized non-Hermitian (not necessarily PT-symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed. Short title: Non-Hermitian oscillator Hamiltonian and su(1,1)

•Nov 21, 2012•12 citations
Re-establishing supersymmetry between harmonic oscillators in D≠1D \neq 1D=1 dimensions
Using a PT symmetric regularization technique we reminad the reader that and how (a) the SUSY is re-established between the two shifted harmonic oscillator potentials V(q)=q2+G/q2+const V(q)=q^2+{G}/{q^2}+ constV(q)=q2+G/q2+const and (b) many non-equivalent Hermitian and non-Hermitian (PT symmetric) systems may often be studied in parallel (with a schematic solvable illustrative example added).
Motivated by the duality of normalizable states and the presence of the quasi-parity quantum number q=+/-1 in PT symmetric (non-Hermitian) quantum mechanical potential models, the relation of PT symmetry and supersymmetry (SUSY) is studied. As an illustrative example the PT invariant version of the Scarf II potential is presented, and it is shown that the "bosonic" Hamiltonian has two different "fermionic" SUSY partner Hamiltonians (potentials) generated from the ground-state solutions with q=1 and q=-1. It is shown that the "fermionic" potentials cease to be PT invariant when the PT symmetry of the "bosonic" potential is spontaneously broken. A modified PT symmetry inspired SUSY construction is also discussed, in which the SUSY charge operators contain the antilinear operator T. It is shown that in this scheme the "fermionic" Hamitonians are just the complex conjugate of the original "fermionic" Hamiltonians, and thus possess the same energy eigenvalues.
Exactly solvable PT\mathcal{PT}PT -symmetric models in two dimensions
Non-Hermitian, PT -symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, PT potentials for a non-relativistic particle confined in a circular geometry. We show that the PT -symmetry threshold can be tuned by introducing a second gain-loss potential or its Hermitian counterpart. Our results explicitly demonstrate that PT breaking in two dimensions has a rich phase diagram, with multiple re-entrant PT -symmetric phases.
The family of metric operators, constructed by Musumbu et al (2007 J. Phys. A: Math. Theor. 40 F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian PT-symmetric part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of generalized non-Hermitian (not necessarily PT-symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed. Short title: Non-Hermitian oscillator Hamiltonian and su(1,1)