Scattering in PT-symmetric quantum mechanics
F. Cannata, J.-P. Dedonder, A. Ventura
TL;DR
This paper develops a formalism for one-dimensional scattering in PT-symmetric quantum mechanics, deriving constraints on transmission and reflection, and explores applications to solvable potentials, highlighting reflectionless potentials and non-local kernel properties.
Contribution
It introduces a new formalism for scattering in non-Hermitian PT-symmetric quantum mechanics and analyzes the properties of reflectionless and non-local potentials.
Findings
Derived constraints on transmission and reflection coefficients for PT-invariant Hamiltonians
Identified conditions for reflectionless potentials with asymptotic PT symmetry
Explored the properties of non-local potentials related to hermiticity and PT invariance
Abstract
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with hermiticity, T invariance and PT invariance.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Topological Materials and Phenomena · Quantum chaos and dynamical systems