Related papers: A note on discrete dynamical systems in theories o…
The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and…
The BPS spectrum of d=4 N=2 field theories in general contains not only hyper- and vector-multipelts but also short multiplets of particles with arbitrarily high spin. This paper extends the method of spectral networks to give an algorithm…
Let $\mathcal{B}(H)$ be the bounded, linear operators on a separable Hilbert space equipped with the norm topology. A property is called typical if the set of operators fulfilling the property is co-meager. We show that having non-empty…
Non-Hermitian topological phenomena occur in mechanical systems described by the Newton equation. A mechanical graphene, which is composed of mass points and springs, shows symmetry-protected exceptional rings (SPERs) in the presence of the…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
By performing explicit computations of correlation functions, we find evidence that there is a sector of the two matrix model defined by the $SU(2)$ sector of ${\cal N}=4$ super Yang-Mills theory, that can be reduced to eigenvalue dynamics.…
We use the functorial properties of Rieffel's pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are…
In the past decade there has been a flurry of activity at the intersection of spectral theory and symplectic geometry. In this paper we review recent results on semiclassical spectral theory for commuting Berezin-Toeplitz and…
By generalizing the algebra of operators of the Asymmetric Simple Exclusion Process (ASEP), a multi-species ASEP in which particles can overtake each other,is defined on both open and closed one dimensional chains. On the ring the steady…
Subject of the paper deals with the perturbation theory of linear operators acting in Hilbert space. For a certain class of perturbations the question is considered about existence of transformation operators implementing linear similarity…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
Let p:N->M be a surjective map of smooth manifolds. We are concerned with singular perturbation problems associated to a pair of second order positive definite differential operators with no zero order terms, that are intertwined by p. We…
The aim of the present manuscript is to develop an index theory for singular Lagrangian systems, with a particular focus on the important class of singular operators given by Bessel type differential operators. The main motivation is to…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
We initiate a systematic study of natural differential operators in Riemannian geometry whose leading symbols are not of Laplace type. In particular, we define a discrete leading symbol for such operators which may be computed pointwise, or…
The weak coupling spectrum of BPS saturated states of pure $N=2$ supersymmetric SU$(n)$ gauge theory is investigated. The method uses known results on the dyon spectrum of the analogous theory with $N=4$ supersymmetry, along with the action…
We study surface and line operators in the GL-twisted N=4 gauge theory in four dimensions. Their properties depend on the parameter t which determines the BRST operator of theory. For t=i we propose a complete description of the 2-category…
We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special…
Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For operators $T$ with at least two points in their…
We introduce a classical limit of the dynamics of quantum spin systems based on coherent states of SU($N$), where $N$ is the dimension of the local Hilbert space. This approach, that generalizes the well-known Landau-Lifshitz dynamics from…