PT-symmetric quantum mechanics
arXiv:2312.17386
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.
arXiv comment58 pages, 35 figures, submitted to Reviews of Modern Physics
Cited by in corpus (48)
- Anti-Parity-Time Symmetric Optics via Flying Atoms
- Observation of higher-order non-Hermitian skin effect
- Supersymmetry and the spontaneous breakdown of PT symmetry
- Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal
- Solitons supported by complex PT symmetric Gaussian potentials
- Nonlinear modal interactions in parity-time () symmetric lasers
- Three-Hilbert-Space Formulation of Quantum Mechanics
- Closed formula for the metric in the Hilbert space of a PT-symmetric model
- On complexified mechanics and coquaternions
- Parity-time symmetry breaking in magnetic systems
- Bound states, scattering states and resonant states in PT-symmetric open quantum systems
- Parity-Time Symmetric Coupled Microresonators with a Dispersive Gain/Loss
- Impact of Dispersive and Saturable Gain/Loss on Bistability of Nonlinear Parity-Time Bragg Gratings
- Scattering in and Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension
- Contrasting Spectral Signatures and Sensitivities of CPA-Lasing in a -Symmetric Periodic Structure
- On integrable wave interactions and Lax pairs on symmetric spaces
- Wave Instabilities and Unidirectional Light Flow in a Cavity with Rotating Walls
- Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories
- Construction of pseudo-bosons systems
- A non-Perturbative and Background-Independent Formulation of Quadratic Gravity
- From Generalized Dirac Equations to a Candidate for Dark Energy
- Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation
- From PT-symmetric quantum mechanics to conformal field theory
- Localized Single Frequency Lasing States in a Finite Parity-Time Symmetric Resonator Chain
- Exceptional points for resonant states on parallel circular dielectric cylinders
- Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians
- On nonlocal models of Kulish-Sklyanin type and generalized Fourier transforms
- Anomalous Parity-Time Symmetry Transition away from an Exceptional Point
- Chebyshev-polynomial expansion of the localization length of Hermitian and non-Hermitian random chains
- Scattering of partially coherent radiation by non-Hermitian localized structures having Parity-Time symmetry
- Unique optical characteristics of a Fabry-Perot resonator with embedded PT-symmetrical grating
- Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate
- Investigation of PT-symmetric Hamiltonian systems from an alternative point of view
- Phase space representation of non-Hermitian system with -symmetry
- Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms
- Quantum Graphs: -symmetry and reflection symmetry of the spectrum
- Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
- Symmetry properties of non-Hermitian PT-symmetric quantum field theories
- Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
- Entire functions with two radially distributed values
- Generalized Nonanalytic Expansions, PT-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators
- Stability boundaries of a Mathieu equation having PT symmetry
- Vector Models in PT Quantum Mechanics
- A Bound on the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential
- Spectra of PT-symmetric Hamiltonians on Tobogganic Contours
- A symmetry perspective of the Riemann zeros
- Faster than Hermitian Time Evolution
- Fall-to-the-centre as a symmetry breaking transition