Solvability and PT-symmetry in a double-well model with point interactions

Abstract

We show that and how point interactions offer one of the most suitable guides towards a quantitative analysis of properties of certain specific non-Hermitian (usually called PT-symmetric) quantum-mechanical systems. A double-well model is chosen, an easy solvability of which clarifies the mechanisms of the unavoided level crossing and of the spontaneous PT-symmetry breaking. The latter phenomenon takes place at a certain natural boundary of the domain of the "acceptable" parameters of the model. Within this domain the model mediates a nice and compact explicit illustration of the not entirely standard probabilistic interpretation of the physical bound states in the very recently developed (so called PT symmetric or, in an alternative terminology, pseudo-Hermitian) new, fairly exciting and very quickly developing branch of Quantum Mechanics.

24 p., written for the special journal issue "Singular Interactions in Quantum Mechanics: Solvable Models". Will be also presented to the int. conference "Pseudo-Hermitian Hamiltonians in Quantum Physics III" (Instanbul, Koc University, June 20 - 22, 2005) http://home.ku.edu.tr/~amostafazadeh/workshop/workshop.htm

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Cited by in corpus (18)

• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• Delta-Function Potential with a Complex Coupling
• Discrete PT-symmetric models of scattering
• Conditional observability
• Coupled-channel version of PT-symmetric square well
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation
• Matching method and exact solvability of discrete PT-symmetric square wells
• Morse potential, symmetric Morse potential and bracketed bound-state energies
• An explicitly solvable model of the spontaneous PT-symmetry breaking
• Exactly solvable models with PT-symmetry and with an asymmetric coupling of channels
• Competing PT potentials and re-entrant PT symmetric phase for a particle in a box
• The spectrum of a Harmonic Oscillator Operator Perturbed by Point Interactions
• Solvable relativistic quantum dots with vibrational spectra
• Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
• Localised nonlinear modes in the PT-symmetric double-delta well Gross-Pitaevskii equation
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Double complex SUSY-transformations: deformations of real potentials and their spectral characteristics
• The large-g observability of the low-lying energies in the strongly singular potentials $V(x)=x^2+g^2/x^6$ after their PT-symmetric regularization