Interactions of Hermitian and non-Hermitian Hamiltonians

Abstract

The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number of soluble models. It is found that in all cases the energy remains real for small values of the coupling constant, but becomes complex if the coupling becomes stronger than some critical value. For a quadratic non-Hermitian PT-symmetric Hamiltonian coupled to an arbitrary real Hermitian PT-symmetric Hamiltonian, the reality of the ground-state energy for small enough coupling constant is established up to second order in perturbation theory.

9 pages, 0 figures

References in corpus (9)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Faster than Hermitian Quantum Mechanics
• Exact PT-Symmetry Is Equivalent to Hermiticity
• Must a Hamiltonian be Hermitian?
• On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model

Cited by in corpus (28)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Nonlinear modes in the harmonic PT-symmetric potential
• Conceptual Problems in Scattering from Localized non-Hermitian Potentials
• Giant amplification of modes in parity-time symmetric waveguides
• On Quantum Tunneling in Real Time
• From self-adjoint to non self-adjoint harmonic oscillators: physical consequences and mathematical pitfalls
• Investigation of non-Hermitian Hamiltonians in the Heisenberg picture
• A longitudinal gauge degree of freedom and the Pais Uhlenbeck field
• A description of pseudo-bosons in terms of nilpotent Lie algebras
• Alternative descriptions and bipartite compound quantum systems
• Investigation of PT-symmetric Hamiltonian systems from an alternative point of view
• Coordinate representation for non Hermitian position and momentum operators
• $\mathcal{D}$ pseudo-bosons in quantum models
• A concise review on pseudo-bosons, pseudo-fermions and their relatives
• Spontaneous breaking of permutation symmetry in pseudo-Hermitian quantum mechanics
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• $\mathcal{P}\mathcal{T}$-Symmetry in Hartree-Fock Theory
• Abstract ladder operators and their applications
• Level Crossings in Complex Two-Dimensional Potentials
• New version of pseudo-hermiticity in the two-sided deformation of Heisenberg algebra
• Artificial Hawking radiation, weak pseudo-Hermiticity and Weyl semimetal blackhole analogy
• Interference of non-Hermiticity with Hermiticity at exceptional points
• Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators
• Swanson Hamiltonian: non-PT-symmetry phase
• Can PT-Symmetric Quantum Mechanics be a Viable Alternative Quantum Theory?
• Simulation of Scalar Field Theories with Complex Actions
• Some invariant biorthogonal sets with an application to coherent states