Perfect transmission scattering as a PT-symmetric spectral problem

Abstract

We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implementing the corresponding quasi-Hermitian quantum mechanical framework from the physical viewpoint. One of the most interesting features of the analysis is that the complex eigenvalues of the underlying non-Hermitian problem, associated with a reflectionless scattering system, lead to the loss of perfect-transmission energies as the parameters characterizing the scattering potential are varied. On the other hand, the scattering data can serve to describe the spectrum of a large class of Schroedinger operators with complex Robin boundary conditions.

7 pages, 5 figures

References in corpus (12)

• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Optical realization of relativistic non-Hermitian quantum mechanics
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• PT-Symmetric Wave Chaos
• Bifurcation diagram and pattern formation in superconducting wires with electric currents
• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
• The resistive state in a superconducting wire: Bifurcation from the normal state
• Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration

Cited by in corpus (24)

• Perspective on topological states of non-Hermitian lattices
• On the metric operator for the imaginary cubic oscillator
• Theory of reflectionless scattering modes
• Breaking of PT-symmetry in bounded and unbounded scattering systems
• Optical waveguide arrays: quantum effects and PT symmetry breaking
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
• Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
• A physical interpretation for the non-Hermitian Hamiltonian
• On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators
• Three solvable matrix models of a quantum catastrophe
• Non-reciprocal mu-near-zero mode in PT-symmetric magnetic domains
• Quantum star-graph analogues of PT-symmetric square wells
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• The Pauli equation with complex boundary conditions
• Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
• On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials
• Scattering off PT-symmetric upside-down potentials
• Electromagnetic Eigenvalue Problems and Nonhermitian Effects in Linear and Saturable Scattering
• Hidden symmetries in non-self-adjoint graphs
• Lax-Phillips scattering theory for PT-symmetric ρ-perturbed operators
• Contact interactions and Kronig-Penney Models in Hermitian and PT-symmetric Quantum Mechanics
• Robustness of perfect transmission resonances to asymmetric perturbation
• The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions