Spectral singularity and non-Hermitian PT-symmetric extension of $A_{N-1}$ type Calogero model without confining potential

Abstract

We consider non-Hermitian PT-symmetric deformation of $A_{N-1}$ 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 wave functions, we found that there exist 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.

10 pages, Latex, No figs, Version to appear J. Phys A: Math. Theor. (Special issue)

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• PT-Symmetric Wave Chaos
• SUSY transformations with complex factorization constants. Application to spectral singularities
• The role of exceptional points in quantum systems

Cited by in corpus (10)

• Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
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• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Various Scattering Properties of a New PT-symmetric non-Hermitian potential
• Deconfinement to Confinement as PT phase transition
• PT phase transition in a (2+1)-d relativistic system
• A black potential for spin less particles
• Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system
• Reciprocity in parity violating non-Hermitian systems
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models