Resonances and continued-fraction Green's functions in non-Hermitian Bose-Hubbard-like quantum models

Abstract

With resonances treated as eigenstates of a non-Hermitian quantum Hamiltonian, the task of localization of the complex energy eigenvalues is considered. The paper is devoted to the reduced version of this task in which one only computes the real quantities called singular values. It is shown that in such an approach (and under suitable constraints including the tridiagonality of the Hamiltdonian) the singular values can be sought as poles of an auxiliary Green's function expressible in terms of a doublet of matrix continued fractions. A family of multi-bosonic Bose-Hubbard-like complex Hamiltonians is recalled for illustration purposes.

31 pp., 3 pictures, all pictures and misprints in Eq. (16) corrected

References in corpus (12)

• Making Sense of Non-Hermitian Hamiltonians
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Non-Markovian Decay and Lasing Condition in an Optical Microcavity Coupled to a Structured Reservoir
• Dynamical regimes of a quantum swap gate beyond the Fermi Golden Rule
• Krylov space approach to Singular Value Decomposition in non-Hermitian systems
• Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics
• Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy
• Quasi-Hermitian formulation of quantum mechanics using two conjugate Schrödinger equations
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation
• Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via $\mathcal{P}\mathcal{T}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Complex tridiagonal quantum Hamiltonians and matrix continued fractions

Cited by in corpus (1)

• Non-Hermitian Bose-Hubbard-like quantum models