Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime

Abstract

A generic PT-symmetric Hamiltonian is assumed tridiagonalized and truncated to N dimensions, and its up-down symmetrized special cases with J=[N/2] real couplings are considered. In the strongly non-Hermitian regime the secular equation gets partially factorized at all N. This enables us to reveal a fine-tuned alignment of the dominant couplings implying an asymptotically sharply spiked shape of the boundary of the J-dimensional quasi-Hermiticity domain in which all the spectrum of energies remains real and observable.

28 pp., 4 tables, 1 figure

References in corpus (7)

• Making Sense of Non-Hermitian Hamiltonians
• Delta-Function Potential with a Complex Coupling
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model
• A return to observability near exceptional points in a schematic PT-symmetric model
• Conditional observability
• Determination of the domain of the admissible matrix elements in the four-dimensional PT-symmetric anharmonic model

Cited by in corpus (27)

• Scattering theory with localized non-Hermiticities
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Gegenbauer-solvable quantum chain model
• Discrete PT-symmetric models of scattering
• Probability-preserving evolution in a non-Hermitian two-band model
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Passage through exceptional point: Case study
• Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
• Discrete quantum square well of the first kind
• PT-symmetric optical superlattices
• Competing PT potentials and re-entrant PT symmetric phase for a particle in a box
• Wheeler-DeWitt equation and the applicability of crypto-Hermitian interaction representation in quantum cosmology
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Exceptional points and domains of unitarity for a class of strongly non-Hermitian real-matrix Hamiltonians
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Paths of unitary access to exceptional points
• On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation
• Classification of the conditionally observable spectra exhibiting central symmetry
• PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring
• Quantum singularities in a solvable toy model
• Few-grid-point simulations of Big Bang singularity in quantum cosmology
• Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models
• Conditional observability versus self-duality in a schematic model
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Interference of non-Hermiticity with Hermiticity at exceptional points
• Exceptional spectrum and dynamic magnetization