We analyze a one-dimensional extended discrete nonlinear Schrödinger (DNLS) dimer model for nonreciprocal wave transmission. The extension corresponds to the addition of a nonlocal or intersite nonlinear response in addition to a purely cubic local (on-site) nonlinear response, which refines the purely cubic model and aligns to more realistic situations. We observe that a diodelike action persists in the extended case; however, the inclusion of nonlocal response tends to reduce the diode action. We show that this extension results in achieving the diode effect at lower incoming intensities as compared to the purely cubic case. We also report that a nearly perfect diode action is possible in the extended case for a higher level of asymmetry between on-site potentials than its cubic counterpart. Moreover, we vary different site-dependent parameters to probe for regimes of a better diode effect within this extended model. We also present the corresponding stability analysis for the exact stationary solutions to the extended DNLS equation, we discuss the bifurcation behavior in detail, and we explicitly give the regions of stability.

One dimensional lattice with an on-site cubic-quintic nonlinear response described by a cubic-quintic discrete nonlinear Schrödinger equation is tested for asymmetric wave propagation. The lattice is connected to linear side chains. Asymmetry is introduced by breaking the mirror symmetry of the lattice with respect to the center of the nonlinear region. Three cases corresponding to dimer, trimer and quadrimer are discussed with focus on the corresponding diode-like effect. Transmission coefficients are analytically calculated for left and right moving waves via backward transfer map. The different transmission coefficients for the left and right moving waves impinging the lattice give rise to a diode-like effect which is tested for different variations in asymmetry and site dependent coefficients. We show that there is a higher transmission for incoming waves with lower wavenumbers as compared to the waves with comparatively larger wavenumbers and a diode-like effect improves by increasing the nonlinear layers. We also show that in the context of transport through such lattices, the cooperation between cubic and quintic nonlinear response is not “additive”. Finally, we numerically analyse Gaussian wave packet dynamics impinging on the CQDNLS lattice for all three cases.

The transmission properties through a saturable cubic-quintic nonlinear defect attached to lateral linear chains is investigated. Particular attention is directed to the possible non-reciprocal diode-like transmission when the parity-symmetry of the defect is broken. Distinct cases of parity breaking are considered including asymmetric linear and nonlinear responses. The spectrum of the transmission coefficient is analytically computed and the influence of the degree of saturation analyzed in detail. The transmission of Gaussian wave-packets is also numerically investigated. Our results unveil that spectral regions with high transmission and enhanced diode-like operation can be achieved.

Supersymmetric quantum mechanical models are computed by the Path integral approach. In the β → 0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants.Explicit computation details are given for the Euler characteristics of the target manifold, and the index of Dirac operator for the model on a spin manifold.

We show that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime. We also connect these entangled particle equations with Finsler geometry. We show that this duality translates strongly coupled quantum equations in the pilot-wave limit to weakly coupled geometric equations.