Discrete PT-symmetric models of scattering

Abstract

One-dimensional scattering mediated by non-Hermitian Hamiltonians is studied. A schematic set of models is used which simulate two point interactions at a variable strength and distance. The feasibility of the exact construction of the amplitudes is achieved via the discretization of the coordinate. By direct construction it is shown that in all our models the probability is conserved. This feature is tentatively attributed to the space- and time-reflection symmetry (a.k.a. PT-symmetry) of our specific Hamiltonians.

17 pp

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• Scattering theory using smeared non-Hermitian potentials
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point
• Hermitian dynamics in a class of pseudo-Hermitian networks
• A physical interpretation for the non-Hermitian Hamiltonian
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• Complete Set of Inner Products for a Discrete PT-symmetric Square-well Hamiltonian
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• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
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• Admissible perturbations and false instabilities in PT-symmetric quantum systems
• Interplay between Fano resonance and $\mathcal{P}\mathcal{T}$ symmetry in non-Hermitian discrete systems
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Coupling-induced nonunitary and unitary scattering in anti-PT-symmetric non-Hermitian systems
• Discrete quantum square well of the first kind
• Scattering properties of anti-parity-time symmetric non-Hermitian system
• Exceptional point induced lasing dynamics in a non-Hermitian system
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Parity-time symmetry under magnetic flux
• Perturbation theory near degenerate exceptional points
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• N-site-lattice analogues of $V(x)=i{x}^3$
• Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation
• Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation
• Interference of non-Hermiticity with Hermiticity at exceptional points
• Parallel dynamics between non-Hermitian and Hermitian systems
• Lax-Phillips scattering theory for PT-symmetric ρ-perturbed operators
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics