TL;DR
This paper investigates one-dimensional scattering using non-Hermitian PT-symmetric Hamiltonians, demonstrating probability conservation through discretized models that simulate point interactions, highlighting the role of PT-symmetry.
Contribution
It introduces a discretized approach to exactly construct scattering amplitudes in PT-symmetric models with point interactions, ensuring probability conservation.
Findings
Probability is conserved in all models
Exact construction of amplitudes is feasible via discretization
PT-symmetry may underpin probability conservation
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.