Related papers: Analytic properties of different unitarization sch…
Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a…
Semi-analytic expressions for the static limit of the T-matrix for electromagnetic scattering are derived for a circular torus, expressed in bases of both toroidal and spherical harmonics. The scattering problem for an arbitrary static…
We study the pattern of activated trajectories in a double well system without detailed balance, in the weak noise limit. The pattern may contain cusps and other singular features, which are similar to the caustics of geometrical optics.…
The properties of a hypergraph explored through the spectrum of its unified matrix was made by the authors in [26]. In this paper, we introduce three different hypergraph matrices: unified Laplacian matrix, unified signless Laplacian…
Recently, a novel model to describe ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ``+'' or ``-'', ``up'' or ``down'', ``yes'' or ``no''), still differing in…
The competition between unretarded dispersion interactions between molecules prevailing at medium range order length scales and their phonon induced coupling at larger scales leads to appearance of nano-scale sub structures in amorphous…
The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…
We prove sharp spectral transition in the arithmetics of phase between localization and singular continuous spectrum for Diophantine almost Mathieu operators. We also determine exact exponential asymptotics of eigenfunctions and of…
We present a universal form of the $T$-matrices renormalized in nonperturbative regime and the ensuing notions and properties that fail conventional wisdoms. A universal scale is identified and shown to be renormalization group invariant.…
It is shown that the simplest multiplicative random complex matrix model generalizes the large-N phase structure found in the unitary case: A perturbative regime is joined to a nonperturbative regime at a point of nonanalyticity.
The alternate row and column scaling algorithm applied to a positive $n\times n$ matrix $A$ converges to a doubly stochastic matrix $S(A)$, sometimes called the \emph{Sinkhorn limit} of $A$. For every positive integer $n$, a two parameter…
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
Electron pairing in one-dimensional binary Hubbard chains is studied for different values of the band-filling using the Density Matrix Renormalization Group method. The systems consist of linear arrays of sites with two types of on-site…
The universal properties of (2 + 1)D topological phases of matter enriched by a symmetry group G are described by G-crossed extensions of unitary modular tensor categories (UMTCs). While the fusion and braiding properties of quasiparticles…
We bring together three key amplification mechanisms in linear dynamical systems: spectral criticality, resonance, and non-normality. We present a unified linear framework that both distinguishes and quantitatively links these effects…
For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…