Time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics in generic non-Hermitian systems

Abstract

$\mathcal{P}\mathcal{T}$-symmetric quantum mechanics has been considered an important theoretical framework for understanding physical phenomena in $\mathcal{P}\mathcal{T}$-symmetric systems, with a number of $\mathcal{P}\mathcal{T}$-symmetry related applications. This line of research was made possible by the introduction of a time-independent metric operator to redefine the inner product of a Hilbert space. To treat the dynamics of generic non-Hermitian systems under equal footing, we advocate in this work the use of a time-dependent metric operator for the inner-product between time-evolving states. This treatment makes it possible to always interpret the dynamics of arbitrary (finite-dimensional) non-Hermitian systems in the framework of time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics, with unitary time evolution, real eigenvalues of an energy observable, and quantum measurement postulate all restored. Our work sheds new lights on generic non-Hermitian systems and spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in particular. We also illustrate possible applications of our formulation with well-known examples in quantum thermodynamics.

9 pages, no figures

References in corpus (15)

• Observation of parity-time symmetry breaking in a single spin system
• New topological invariants in non-Hermitian systems
• The Naimark dilated PT-symmetric brachistochrone
• Time-dependent version of cryptohermitian quantum theory
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Time evolution of non-Hermitian Hamiltonian systems
• Geometric classification of non-Hermitian topological systems through the singularity ring
• Jarzynski equality in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics
• Quantum Geometric Tensor in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• PT spectroscopy of the Rabi problem
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Energy Observable for a Quantum System with a Dynamical Hilbert Space and a Global Geometric Extension of Quantum Theory
• Quantum Work Relations and Response Theory in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Systems
• Holonomic Gates in Pseudo-Hermitian Quantum Systems
• Links between Dissipation and Rényi Divergences in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics

Cited by in corpus (27)

• Non-Hermitian Floquet Topological Matter -- A Review
• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• $\mathcal{P}\mathcal{T}$-symmetric, non-Hermitian quantum many-body physics -- a methodological perspective
• Floquet engineering and simulating exceptional rings with a quantum spin system
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Uncertainty Relation for Non-Hermitian Systems
• Observing a Changing Hilbert-Space Inner Product
• The effect of thermal photons on exceptional points in coupled resonators
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Formation of Exceptional Points in pseudo-Hermitian Systems
• Solvable dilation model of $\mathcal{P}\mathcal{T}$-symmetric systems
• Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{P}\mathcal{T}$ symmetry
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
• Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems
• Real energies and Berry phases in all PT-regimes in time-dependent non-Hermitian theories
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Enhanced frequency and temperature estimation by a $\mathcal{P}\mathcal{T}$-symmetric quantum oscillator
• Quantum thermodynamics aspects with a thermal reservoir based on $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Analytical Study of the Non-Hermitian Semiclassical Rabi Model
• Imaginary spin-orbital coupling in parity-time symmetric systems with momentum-dependent gain and loss
• Emerging (2+1)D electrodynamics and topological instanton in pseudo-Hermitian two-level systems
• Topological state permutations in time-modulated non-Hermitian multiqubit systems with suppressed non-adiabatic transitions
• Stronger sum uncertainty relations for non-Hermitian operators
• To quantify the difference of $\eta$-inner products in $\mathcal{P}\mathcal{T}$-symmetric theory
• Floquet multiple exceptional points with higher-order skin effect
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers