Topological edge modes in one-dimensional photonic systems are usually studied considering the interface between two different semi-infinite periodic crystals (PCs) with inverted band structure around Dirac point. Here we consider case where PCs finite, constituting an open scattering system, and study influence of size this finite on mode by inspecting complex resonances. First show resonance distribution corresponding to inversion Perturbations from point display emergence localized mode....

We develop a classification of perfectly transmitting resonances occurring in effectively one-dimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries the medium shown to yield piecewise translation-invariant quantities, used distinguish with arbitrary field profile from following symmetries. Focusing on light scattering aperiodic multilayer structures, we demonstrate this for representative setups, providing insight origin perfect...

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries shown yield invariant currents that characterize wave propagation. These map function from an arbitrary spatial domain any symmetry-related domain. Our approach addresses combination local symmetries, thus applying in particular acoustic, optical matter waves. Nonvanishing values provide a systematic pathway breaking discrete symmetries.

We consider the non-Hermitian, parity-time (PT) symmetric extensions of one-dimensional Su-Schrieffer-Heeger (SSH) model in topological non-trivial configuration. study properties topologically protected edge states, and develop an effective two-state analytical description system that accurately predicts PT-symmetry breaking point for states. verify our results by exact numerical calculations.

Dominant energy subspaces of statistical systems are defined with the help restrictive conditions on various characteristics distribution, such as probability density and fourth order Binder's cumulant. Our analysis generalizes ideas critical minimum subspace (CRMES) technique, applied previously to study specific heat's finite-size scaling. Here, we illustrate alternatives that useful for further anomalies behavior corresponding dominant is presented two-dimensional (2D) Baxter-Wu 2D 3D...

We introduce the concept of parity symmetry in restricted spatial domains -- local and explore its impact on stationary transport properties generic, one-dimensional aperiodic potentials compact support. It is shown that, each domain potential, there exists an invariant quantity form a non-local current, addition to globally probability current. For symmetrically incoming states, both currents vanish if weak commutation total operator with Hamiltonian established, leading eigenstates....

We consider a periodic waveguide array whose unit cell consists of $\mathcal{PT}$-symmetric quadrimer with two competing loss/gain parameter pairs which lead to qualitatively different symmetry-broken phases. It is shown that the transitions between phases are described by symmetry-adapted nonlocal current maps spectral properties spatially resolved field, for lattice as well isolated quadrimer. Its site-average acts like natural order general class one-dimensional Hamiltonians, vanishing in...

We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite presence losses, existence a spatially invariant current is shown theoretically and observed experimentally. demonstrate how this leads to generalization Bloch parity theorems for systems defining mapping pressure field between symmetry-related spatial domains. Using experimental data, we verify with remarkable accuracy. For performed experiment, employ construction technique based on symmetries that...

Recently [Phys. Rev. Lett. {\bf 106}, 093902 (2011)] it has been shown that $\mathcal{PT}$-symmetric scattering systems with balanced gain and loss, undergo a transition from eigenstates, which are norm preserving, to symmetry broken pairs of eigenstates exhibiting net amplification loss. In the present work we derive existence an invariant non-local current can be directly associated observed playing role "order parameter". The use this for description $\mathcal{PT}$-symmetry breaking...

A recursive scheme for the design of scatterers acting simultaneously as emitters and absorbers, such lasers coherent perfect absorbers in optics, at multiple prescribed frequencies is proposed. The approach based on assembly non-Hermitian emitter absorber units into self-dual emitter-absorber trimers different composition levels, exploiting simple structure corresponding transfer matrices. In particular, lifting restriction to parity-time-symmetric setups enables realization action distinct...

A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of stationary Schrödinger equation. The potential are encoded into corresponding basis vectors in terms symmetry-induced two-point invariant currents which map amplitudes between symmetry-related points. universal wavefunction structure locally symmetric potentials revealed, independently physical boundary conditions, by using special bases adapted to...

We study a two-species mixture of exciton-polaritons with self- and cross-interaction nonlinearities in double-well structure, the presence relaxation continuous pumping. identify conditions that render system parity-time symmetric, investigate its dynamic static properties. show can exhibit long-term coherent oscillations populations two polaritonic components between potential wells, simulate dynamics pair spin-1/2 particles (qubits) exchange interaction.

A variational scheme for the derivation of generalized, symmetry-induced continuity equations Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields whose global invariance under dilation phase variations leads to mixed equation fields. In combination with discrete spatial symmetries underlying Hamiltonian, shown produce bilocal conservation laws single field. This generalized conserved charges vanishing boundary...

A field-theoretical approach to the scattering off an oscillating quantum system is developed. As a key ingredient it employs adiabatic eigenstate basis and consists of perturbative scheme for calculation geometric phases influencing transmission through time-dependent potential landscape. The main advantage identification basic diagrams which allow immediate interpretation underlying elementary physical processes contributing behavior. We apply our method simple, but prototypical, problem...

We investigate the dynamics and stationary states of a semiconductor exciton-polariton condensate in double well potential. find that upon population build up polaritons by above-threshold laser pumping, coherence relaxation due to phase fluctuations drives system into stable fixed point corresponding self-organized PT-symmetric phase.

We investigate the perfect transmission resonances (PTRs) of perturbed 1D finite periodic systems with mirror symmetric cells. The unperturbed scattering region consists $N$ identical cells and related spectrum possesses at least $N-1$ PTRs in each pass band Bloch dispersion unit cell. On other hand, perturbation is breaking periodicity and, a priori, able to eliminate all PTRs. show how could still appear case suitable design perturbation. also reveal connection between two apparently...

Received 15 October 2014DOI:https://doi.org/10.1103/PhysRevA.90.049903©2014 American Physical Society