Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
arXiv:1506.00216 · doi:10.1016/j.aop.2015.06.019
Abstract
Discrete multiparametric 1D quantum well with PT-symmetric long-range boundary conditions is proposed and studied. As a nonlocal descendant of the square well families endowed with Dirac (i.e., Hermitian) and with complex Robin (i.e., non-Hermitian but still local) boundary conditions, the model is shown characterized by the survival of solvability in combination with an enhanced spectral-design flexibility. The solvability incorporates also the feasibility of closed-form constructions of the physical Hilbert-space inner products rendering the time-evolution unitary.
arXiv comment32 pages, 9 figures
References in corpus (27)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- Pseudo-Hermitian Representation of Quantum Mechanics
- Physical Aspects of Pseudo-Hermitian and -Symmetric Quantum Mechanics
- Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
- Entanglement and spin squeezing in non-Hermitian phase transitions
- Local PT symmetry violates the no-signaling principle
- Robust and fragile PT-symmetric phases in a tight-binding chain
- Scattering in PT-symmetric quantum mechanics
- Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential
- Closed formula for the metric in the Hilbert space of a PT-symmetric model
- Conceptual Problems in Scattering from Localized non-Hermitian Potentials
- Bound states in the continuum in PT-symmetric optical lattices
- Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices
- Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation
- 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
- Perfect transmission scattering as a PT-symmetric spectral problem
- Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
- Hermitian scattering behavior for the non-Hermitian scattering center
- On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators
- Matching method and exact solvability of discrete PT-symmetric square wells
- Spiked potentials and quantum toboggans
- Discrete quantum square well of the first kind
- Quantum inner-product metrics via recurrent solution of Dieudonne equation
- Solvable non-Hermitian discrete square well with closed-form physical inner product
- On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials
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- PT-symmetric Rabi model: Perturbation theory
- Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation
- Parity-time symmetry under magnetic flux
- Hybrid form of quantum theory with non-Hermitian Hamiltonians
- Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
- Quantization of Big Bang in crypto-Hermitian Heisenberg picture