PT-symmetric model with an interplay between kinematical and dynamical non-localities

2014/10/31 by Miloslav Znojil
Physics and Astronomy · #Advanced Differential Geometry Research #Dynamical systems theory #Measure (data warehouse) #Nonlinear Waves and Solitons #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum system #quant-ph

paper · pdf · doi:10.1088/1751-8113/48/19/195303

published as J. Phys. A: Math. Theor. 48 (2015) 195303 · 21 pages, 5 figures

arxiv created 2015/03/31 · openalex publication_date 2015/04/22 · arxiv updated 2015/04/24 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05

Abstract

A new family of non-Hermitian -symmetric quantum models is proposed in which the Hamiltonians are finite-dimensional and in which the dynamical-input potential V is multi-parametric and non-local. The choice is supported by the exact solvability of Schrödinger equation and by the well known fact that in -symmetric models a non-locality is already present due to the generic kinematical non-diagonality of the Hermitizing metrics Θ . For a subfamily of our H s, also all of the eligible metrics Θ appear obtainable in closed form.

Citations

• Discrete quantum square well of the first kind
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential
• Making sense of non-Hermitian Hamiltonians
• General Theory of Spin-Wave Interactions
• Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
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