Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians

Abstract

We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasi-Hermitian Hamiltonian are related to the symmetry generators of an equivalent Hermitian Hamiltonian.

6 pages, published version

References in corpus (4)

• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Time evolution of non-Hermitian Hamiltonian systems
• Isospectral Hamiltonians from Moyal products
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation

Cited by in corpus (11)

• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes
• Exceptional points in oligomer chains
• $\mathcal{D}$-deformed harmonic oscillators
• Dynamical control of solitons in a parity-time-symmetric coupler by periodic management
• Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories
• Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation
• Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity
• Infinite series of time-dependent Dyson maps
• Swanson Hamiltonian: non-PT-symmetry phase