PT-symmetric quantum systems with positive P

Abstract

A new version of PT-symmetric quantum theory is proposed and illustrated by an N-site-lattice Legendre oscillator. The essence of the innovation lies in the replacement of parity P (serving as an indefinite metric in an auxiliary Krein space) by its non-involutory alternative P(positive)=Q>0 playing the role of a positive-definite nontrivial metric in an auxiliary, redundant, unphysical Hilbert space. It is shown that the QT-symmetry of this form remains appealing and technically useful.

13 pp

References in corpus (16)

• Making Sense of Non-Hermitian Hamiltonians
• The ODE/IM Correspondence
• Quantum noise and self-sustained radiation of PT-symmetric systems
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• Chirality of wave functions for three coalescing levels
• Gegenbauer-solvable quantum chain model
• A return to observability near exceptional points in a schematic PT-symmetric model
• Complex Lagrangians and phantom cosmology
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• Complete Set of Inner Products for a Discrete PT-symmetric Square-well Hamiltonian
• Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Discrete quantum square well of the first kind
• On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator
• Particles versus fields in PT-symmetrically deformed integrable systems

Cited by in corpus (8)

• Multiply Degenerate Exceptional Points and Quantum Phase Transitions
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation
• Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians
• Systematics of quasi-Hermitian representations of non-Hermitian quantum models
• Quantization of Big Bang in crypto-Hermitian Heisenberg picture
• Mathematical and physical meaning of the crossings of energy levels in $\mathcal{P}\mathcal{T}-$symmetric systems
• Quantum mechanics using two auxiliary inner products