Linear quench of the transverse field drives quantum Ising chain across a critical point from paramagnetic to ferromagnetic phase. We focus on normal and anomalous quadratic correlators between fermionic kink creation annihilation operators. They depend not only Kibble-Zurek (KZ) correlation length but also dephasing scale, which differs KZ by logarithmic correction. Additional slowing down ram...

A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in the nonlinear Schrödinger equation. This is achieved by considering interactions among four Fourie...

We examine the convective stability of hydrodynamic discs with full stratification in the local approximation and in the presence of thermal diffusion (or relaxation). Various branches of the relevant axisymmetric dispersion relation derived by Urpin are discussed. We find that when the vertical Richardson number is larger than or equal to the radial one (i.e. |Riz| ≥ |Rix|) and wavenumbers are...

We reconsider the earlier found solutions of the Knizhnik-Zamolodchikov (KZ) equations describing correlators based on the admissible representations of A (1) 1. Exploiting a symmetry of the KZ equations we show that the original innnite sums representing the 4-point chiral correlators can be eeectively summed up. Using these simpliied expressions with proper choices of the contours we determin...

The spin vortices are shown to be created through the Kibble-Zurek (KZ) mechanism in a quantum phase transition of a spin-1 ferromagnetic Bose-Einstein condensate, when the applied magnetic field is quenched below a critical value. It is shown that the magnetic correlation functions have finite correlation lengths, and magnetizations at widely separated positions grow in random directions, resu...

Lattice reduction (LR) aided multiple-inputmultiple-out (MIMO) linear detection can achieve the maximum receive diversity of the maximum likelihood detection (MLD). By emloying the most commonly used Lenstra, Lenstra, and L. Lov ́asz (LLL) algorithm, an equivalent channel matrix which is shorter and nearly orthogonal is obtained. And thus the noise enhancement is greatly reduced by employing the...

Weyl points, as monopoles of Berry curvature in momentum space, have captured much attention recently in various branches of physics. Realizing topological materials that exhibit such nodal points is challenging and indeed, Weyl points have been found experimentally in transition metal arsenide and phosphide and gyroid photonic crystal whose structure is complex. If realizing even the simplest ...

This work presents a systematic method to successively minimize the state complexity of the self-dual lattices (in the sense that each section of the trellis has the minimum possible number of states fixing its preceding co-ordinates). This is based on representing the lattice on an orthogonal co-ordinate system corresponding to the Gram-Schmidt (GS) vectors of a Korkin-Zolotarev (KZ) reduced b...

We reconsider the earlier found solutions of the Knizhnik-Zamolodchikov (KZ) equations describing correlators based on the admissible representations of A (1) 1. Exploiting a symmetry of the KZ equations we show that the original innnite sums representing the 4-point chiral correlators can be eeectively summed up. Using these simpliied expressions with proper choices of the contours we determin...

The resonant optical modes of a high permittivity dielectric prism with an equilateral triangular cross section are discussed. Eigenmode solutions of the scalar Helmholtz equation with Dirichlet boundary conditions, appropriate to a conducting boundary, are applied for this purpose. The particular plane wave components present in these modes are analyzed for their total internal reflection beha...