Related papers: Local symmetries in one-dimensional quantum scatte…
We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of…
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…
We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite the presence of losses, the existence of a spatially invariant current is shown theoretically and observed experimentally. We demonstrate how this…
We develop a classification of perfectly transmitting resonances occuring in effectively one-dimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries of the medium are shown to yield…
We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schr\"odinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The…
A general formalism is worked out for the description of one-dimensional scattering by non-local separable potentials and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
We explore wave-mechanical scattering in two spatial dimensions assuming that the corresponding potential is invariant under linear symmetry transforms such as rotations, reflections and coordinate exchange. Usually the asymptotic…
A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the ranges and axes of local reflection symmetry…
Non-Hermitian, one-dimensional potentials which are also non-local, allow for scattering asymmetries, namely, asymmetric transmission or reflection responses to the incidence of a particle from left or right. The symmetries of the potential…
We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
Parity-Time ($\mathcal{PT}$) symmetry has become an important concept in the design of synthetic optical materials, with exotic functionalities such as unidirectional transport and non-reciprocal reflection. At exceptional points, this…
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function…
It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…
A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schr\"odinger equation. The local symmetries of the potential are encoded into…
Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial…
"Punchets" are hybrids between ratchets and pumps, combining a spatially periodic static potential, typically asymmetric under space inversion, with a local driving that breaks time-reversal invariance, and are intended to model metal or…
We study the scattering properties of $N$ identical one-dimensional localized $\mathcal{PT}$-symmetric potentials, connected in series as well as in parallel. We derive a general transfer matrix formalism for parallel coupled quantum…
The nonlocal properties for a kind of generic N-dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. It is shown that two generic density matrices are locally…
For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT) transformation. We determine the…