Scattering in PT-symmetric quantum mechanics

Abstract

A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with hermiticity, T invariance and PT invariance.

41 pages, to appear in Ann. Phys

References in corpus (2)

• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Strengthened PT-symmetry with P $\ne$ P${}^{†}$

Cited by in corpus (60)

• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures
• PT-Symmetric Electronics
• Invisibility in PT-symmetric complex crystals
• Optical realization of relativistic non-Hermitian quantum mechanics
• Quantum noise and self-sustained radiation of PT-symmetric systems
• Bifurcation diagram and pattern formation in superconducting wires with electric currents
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Incident Direction Independent Wave Propagation and Unidirectional Lasing
• Theory of reflectionless scattering modes
• Invisibility in non-Hermitian tight-binding lattices
• Conceptual Problems in Scattering from Localized non-Hermitian Potentials
• Unidirectional zero sonic reflection in passive $\mathcal{P}\mathcal{T}$ symmetric Willis media
• Breaking of PT-symmetry in bounded and unbounded scattering systems
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
• Parity-time symmetry in optical microcavity systems
• Scattering theory with localized non-Hermiticities
• Regularization of the spectral singularity in $\mathcal{P}\mathcal{T}$-symmetric systems by all order nonlinearities: Nonreciprocity and optical isolation
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Supersymmetry generated one-way invisible PT-symmetric optical crystals
• New supersymmetry-generated complex potentials with real spectra
• Reciprocal and unidirectional scattering of parity-time symmetric structures
• Discrete PT-symmetric models of scattering
• Asymmetric transmission through a flux-controlled non-Hermitian scattering center
• Scattering theory using smeared non-Hermitian potentials
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Invisible defects in complex crystals
• Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
• Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential
• Non-Hermitian interferometer: Unidirectional amplification without distortion
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• The resistive state in a superconducting wire: Bifurcation from the normal state
• Scattering in the PT-symmetric Coulomb potential
• Spectral singularity and deep multiple minima in the reflectivity in non-Hermitian (complex) Ginocchio potential
• Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
• Scattering properties of anti-parity-time symmetric non-Hermitian system
• $S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians
• Overcritical PT-symmetric square well potential in the Dirac equation
• A unidirectional invisible PT-symmetric complex crystal with arbitrary thickness
• Coherent perfect absorption with and without lasing in complex potentials
• Unitary Scattering Protected by Pseudo-Hermiticity
• Conserved Correlation in PT -symmetric Systems: Scattering and Bound States
• Generalized Parametric Space, Parity Symmetry of Reflection, and Systematic Design Approach for Parity-Time Symmetric Photonic Systems
• Helical resonant transport and purified amplification at an exceptional point
• Kinematic and dynamic vortices in a thin film driven by an applied current and magnetic field
• Absence of Floquet scattering in oscillating non-Hermitian potential wells
• Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• Scattering states of a particle, with position-dependent mass, in a $\mathcal{P}\mathcal{T}$ symmetric heterojunction
• Origin of branch points in the spectrum of PT-symmetric periodic potentials
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Coherent scattering from semi-infinite non-Hermitian potentials
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation
• Spectral Singularities with Directional Sensitivity
• Scattering in a varying mass PT symmetric double heterojunction
• Lax-Phillips scattering theory for PT-symmetric ρ-perturbed operators