Detecting Broken PT-Symmetry

Abstract

A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system `respects' this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to algorithmically detect the existence of complex eigenvalues for a given PT-symmetric matrix. The procedure uses classical results from stability theory which qualitatively locate the zeros of real polynomials in the complex plane. The interest and value of the present approach lies in the fact that it avoids diagonalization of the Hamiltonian at hand.

8 pages

Cited by in corpus (10)

• Making Sense of Non-Hermitian Hamiltonians
• The ODE/IM Correspondence
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
• A return to observability near exceptional points in a schematic PT-symmetric model
• Determination of the domain of the admissible matrix elements in the four-dimensional PT-symmetric anharmonic model
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• Nonlinear stationary states in PT-symmetric lattices