The Horizons of Observability in PT-symmetric Four-site Quantum Lattices

M. Znojil

Abstract


One of the key merits of PT-symmetric (i.e., parity times time reversal symmetric) quantum Hamiltonians H lies in the existence of a horizon of the stability of the system. Mathematically speaking, this horizon is formed by the boundary of the domain D(H) ⊂ RD of the (real) coupling strengths for which the spectrum of energies is real and non-degenerate, i.e., in principle, observable. It is shown here that even in the elementary circular four-site quantum lattices with D = 2 or D = 3 the domain of hidden Hermiticity D(H) proves multiply connected, i.e., topologically nontrivial.

Keywords


hidden Hermiticity; spectra and exceptional points; horizons; discrete Schroedinger operators; quantum graphs; loops; four-site lattices; connectedness; strong-coupling anomalies

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague