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Pseudo supersymmetric partners for the generalized Swanson model

Anjana Sinha, Pinaki Roy

New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., , where α, β are real constants, with α ≠ β, and and are generalized creation and annihilation operators. It is shown that the initial Hamiltonian H − , and its partner H + , are related by pseudo supersymmetry, and they share all the eigen energies except for the ground state. This pseudo supersymmetric extension enlarges the class of non Hermitian Hamiltonians H ± , related to their respective Hermitian counterparts h ± , through the same similarity transformation operator ρ: H ± = ρ −1 h ± ρ. The formalism is applied to the entire class of shape-invariant models.New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., , where α, β are real constants, with α ≠ β, and and are generalized creation and annihilation operators. It is shown that the initial Hamiltonian H − , and its partner H + , are related by pseudo supersymmetry, and they share all the eigen energies except for the ground state. This pseudo supersymmetric extension enlarges the class of non Hermitian Hamiltonians H ± , related to their respective Hermitian counterparts h ± , through the same similarity transformation operator ρ: H ± = ρ −1 h ± ρ. The formalism is applied to the entire class of shape-invariant models.

arXiv:0806.4490Journal of Physics A Mathematical and TheoreticalJul 22, 200819 citations

On Supersymmetric Quantum Mechanics

M. Kibler, Mohammed Daoud A

Springer eBooksJan 1, 20043 citations

Supersymmetric Quantum Mechanics

Asim Gangopadhyaya, Jeffry V. Mallow A, Constantin Rasinariu

WORLD SCIENTIFIC eBooksOct 1, 201038 citations

Deconstructing non-Dirac–Hermitian supersymmetric quantum systems

Pijush K Ghosh

A method to construct a non-Dirac–Hermitian supersymmetric quantum system that is isospectral with a Dirac–Hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving both bosonic and fermionic degrees of freedom in terms of non-Dirac–Hermitian operators which are Hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. A pseudo-Hermitian realization of the Clifford algebra for a pre-determined positive-definite metric is used to construct supersymmetric systems with one or many degrees of freedom. It is shown that exactly solvable non-Dirac–Hermitian supersymmetric quantum systems can be constructed corresponding to each exactly solvable Dirac–Hermitian system. Examples of non-Dirac–Hermitian (i) non-relativistic Pauli Hamiltonian, (ii) super-conformal quantum system, and (iii) supersymmetric Calogero-type models admitting entirely real spectra are presented.A method to construct a non-Dirac–Hermitian supersymmetric quantum system that is isospectral with a Dirac–Hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving both bosonic and fermionic degrees of freedom in terms of non-Dirac–Hermitian operators which are Hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. A pseudo-Hermitian realization of the Clifford algebra for a pre-determined positive-definite metric is used to construct supersymmetric systems with one or many degrees of freedom. It is shown that exactly solvable non-Dirac–Hermitian supersymmetric quantum systems can be constructed corresponding to each exactly solvable Dirac–Hermitian system. Examples of non-Dirac–Hermitian (i) non-relativistic Pauli Hamiltonian, (ii) super-conformal quantum system, and (iii) supersymmetric Calogero-type models admitting entirely real spectra are presented.

arXiv:1101.2120Journal of Physics A Mathematical and TheoreticalMay 3, 201110 citations

Bi-orthogonal quantum mechanics related to T -pseudo-Hermitian Rashba Hamiltonian

Arindam Chakraborty

Abstract A non-Hermitian version of Rashba Hamiltonian has been introduced. The said Hamiltonian is found to be pseudo-Hermitian under fermionic time-reversal and its eigen-states show a kind of two-parameter-bi-orthogonality. The possibility of an equivalent version of Kramers’ degeneracy theorem has been explored and the supersymmetric and pseudo-supersymmetric structures relating to the present system are also discussed.

Physica ScriptaMay 2, 20250 citations

Supersymmetric quantum mechanics

Georg Junker

Institute of Physics eBooksJan 1, 20191 citation

Pseudo-supersymmetric quantum mechanics and isospectral pseudo-Hermitian Hamiltonians

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