Infinite series of time-dependent Dyson maps

Abstract

We propose and explore a scheme that leads to an infinite series of time- dependent Dyson maps which associate different Hermitian Hamiltonians to a uniquely specified time-dependent non-Hermitian Hamiltonian. We identify the underlying sym- metries responsible for this feature respected by various Lewis-Riesenfeld invariants. The latter are used to facilitate the explicit construction of the Dyson maps and metric oper- ators. As a concrete example for which the scheme is worked out in detail we present a two-dimensional system of oscillators that are coupled to each other in a non-Hermitian PT -symmetrical fashion

arXiv comment16 pages

References in corpus (18)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermitian Representation of Quantum Mechanics
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Time-dependent version of cryptohermitian quantum theory
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Unitary quantum evolution for time-dependent quasi-Hermitian systems with non-observable Hamiltonians
• Time evolution of non-Hermitian Hamiltonian systems
• Time Dependent $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• On the invariant method for the time-dependent non-Hermitian Hamiltonians
• Non-Hermitian Hamiltonians of Lie algebraic type
• Solvable two dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• Adiabatic time-dependent metrics in PT-symmetric quantum theories
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• Exactly solvable time-dependent non-Hermitian quantum systems from point transformations
• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• Time-independent approximations for time-dependent optical potentials
• Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems

Cited by in corpus (5)

• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
• IR/UV mixing from local similarity maps of scalar non-Hermitian field theories
• Solvable dilation model of $\mathcal{P}\mathcal{T}$-symmetric systems
• Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories
• Real energies and Berry phases in all PT-regimes in time-dependent non-Hermitian theories