Related papers: Ergodic Theory Meets Polarization. I: An Ergodic T…
We prove that for an arbitrary indexing group, every ergodic infinitely divisible stationary process that is separable in probability is weakly mixing. This shows that, as in the well-known case of Gaussian stationary processes, ergodicity…
The symmetry conditions for the development of a macroscopic electrical polarization as a secondary order parameter to a magnetic ordering transition, and the constraints on the direction of the polarization vector, are determined by a…
We study a so-called semi-ergodic brickwork dual-unitary circuits where, in the infinite volume limit, the two-point correlation functions of single-site operators exhibit ergodic behavior along one light ray and non-ergodic behavior along…
We describe the mechanism by which a metamaterial surface can act as an ideal phase-controlled rotatable linear polarizer. With equal-power linearly polarized beams incident on each side of the surface, varying the relative phase rotates…
At large, most animal brains present two mirror-symmetric sides; but closer inspection reveals a range of asymmetries (in shape and function), that seem more salient in more cognitively complex species. Sustaining symmetric, redundant…
Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the analysis and construction of polar codes involve the complex iterative-calculation. In…
Polar encoding, described by Arikan in IEEE Transactions on Information Theory, Vol. 55, No. 7, July 2009, was a milestone for telecommunications. A Polar code distributes information among high and low-capacity channels, showing the…
We derive an expression for the local transverse polarization of a boost-invariant expanding system of massive particles, which involves a set of dynamical spin moments. Starting from spin kinetic theory, we obtain a closed set of equations…
Regulation to a well-defined target state is a fundamental requirement for achieving reliable functionality in living systems and maintaining specific non-equilibrium states. The control of certain properties and functionalities of systems…
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…
The photon-induced process of electron-positron pair creation in a strong homogeneous magnetic field, provided that the polarization of particles is arbitrary, has been considered. The polarization of a photon is described in terms of the…
A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the…
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for…
Thermodynamic theory is developed for the ferroelectric phase transition of an ultrathin film in equilibrium with a chemical environment that supplies ionic species to compensate its surface. Equations of state and free energy expressions…
We develop a general theory of electric polarization induced by inhomogeneity in crystals. We show that contributions to polarization can be classified in powers of the gradient of the order parameter. The zeroth order contribution reduces…
In this paper, we elaborate ring theoretic properties of nodal orders. In particular, we prove that they are closed under taking crossed products with finite groups.
On the one hand, electromagnetic dual particles preserve the helicity of light upon interaction. On the other hand, chiral particles respond differently to light of opposite helicity. These two properties on their own constitute a source of…
This paper studies the problem of stabilizing target formations specified by inter-neighbor bearings with relative position measurements. While the undirected case has been studied in the existing works, this paper focuses on the case where…
We review how some multianalytic inner functions of the Beurling type theorem are associated to row contractions following works of G.Popescu. Motivated by a result on weak Markov dilations, we define a notion of characteristic function for…
A decoding algorithm for polar (sub)codes with binary $2^t\times 2^t$ polarization kernels is presented. It is based on the window processing (WP) method, which exploits the linear relationship of the polarization kernels and the Arikan…