Asymmetric wave transmission through one dimensional lattices with cubic-quintic nonlinearity

One dimensional lattice with an on-site cubic-quintic nonlinear response described by a cubic-quintic discrete nonlinear Schr\"odinger 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.Comment: 10 pages, 17 figure

Two particle entanglement and its geometric duals

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.Comment: 10pp, Typos corrected, Accepted versio

Present and future of neurology in pakistan

Neurology started as a department in early nineteen sixties in Dow Medical College and King Edward Medical College and initially having a separate department of neurology was not mandated in medical colleges by Pakistan Medical and Dental Council¹. Some neurology training programs do not give exposure to subspecialties and training is focused on adult neurology². From 2015 to 2016, several conferences were held on neurology including an Annual Meeting in Quetta, movement disorder conference in Lahore