PT-symmetric quantum mechanics

Abstract

It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define a physically acceptable quantum-mechanical system even if the Hamiltonian is not Hermitian. The study of PT-symmetric quantum systems is a young and extremely active research area in both theoretical and experimental physics. The purpose of this Review is to provide established scientists as well as graduate students with a compact, easy-to-read introduction to this field that will enable them to understand more advanced publications and to begin their own theoretical or experimental research activity. The ideas and techniques of PT symmetry have been applied in the context of many different branches of physics. This Review introduces the concepts of PT symmetry by focusing on elementary one-dimensional PT-symmetric quantum and classical mechanics and relies in particular on oscillator models to illustrate and explain the basic properties of PT-symmetric quantum theory.

58 pages, 35 figures, submitted to Reviews of Modern Physics

Cited by in corpus (12)

• Three-Hilbert-Space Formulation of Quantum Mechanics
• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• Parity-Time Symmetric Coupled Microresonators with a Dispersive Gain/Loss
• Contrasting Spectral Signatures and Sensitivities of CPA-Lasing in a $\mathcal{P}\mathcal{T}$-Symmetric Periodic Structure
• From Generalized Dirac Equations to a Candidate for Dark Energy
• On nonlocal models of Kulish-Sklyanin type and generalized Fourier transforms
• Unique optical characteristics of a Fabry-Perot resonator with embedded PT-symmetrical grating
• Quantum Graphs: $\mathcal{P}\mathcal{T}$-symmetry and reflection symmetry of the spectrum
• Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
• Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
• A symmetry perspective of the Riemann zeros
• Faster than Hermitian Time Evolution