Related papers: Critical lattices, elliptic curves and their possi…
Lattice models allow for a computationally efficient investigation of motility-induced phase separation (MIPS) compared to off-lattice systems. Simulations are less demanding and thus bigger systems can be accessed with higher accuracy and…
Critical points of classical and quantum lattice models are often described by scale-invariant Lifshitz theories which are anisotropic in the continuum limit, as characterized by a dynamical critical exponent $z\neq1$. This type of critical…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
We argue that the presence of \emph{any} exact $U(1)$ higher-form symmetry, under mild assumptions, presents a fundamental obstruction to ergodicity under unitary dynamics in lattice systems with local interactions and finite on-site…
We evaluate the determinant of a matrix whose entries are elliptic hypergeometric terms and whose form is reminiscent of Sylvester matrices. A hypergeometric determinant evaluation of a matrix of this type has appeared in the context of…
A general elliptic $N\times N$ matrix Lax scheme is presented, leading to two classes of elliptic lattice systems, one which we interpret as the higher-rank analogue of the Landau-Lifschitz equations, while the other class we characterize…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from…
We establish the existence and nonexistence of entire solutions to a semilinear elliptic problem whose nonlinearity is the critical power multiplied by a function that takes the value 1 in an open bounded region and the value -1 in its…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the weak solutions in domains satisfying the so-called…
We define auto- and cross-correlation functions capable to capture dynamical characteristics induced by local phase space structures in a general dynamical system. These correlation functions are calculated in the Standard Map for a range…
Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…
This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
We introduce a direct generalization of the Weinstein conjecture to closed, Lichnerowicz exact, locally conformally symplectic manifolds, (for short $\lcs$ manifolds). This conjectures existence of certain 2-curves in the manifold, which we…
In the general context of computable metric spaces and computable measures we prove a kind of constructive Borel-Cantelli lemma: given a sequence (constructive in some way) of sets $A_{i}$ with effectively summable measures, there are…
A mathematical modeling process for phenomena with a single state variable that attempts to be realistic must be given by a scalar nonautonomous differential equation $x'=f(t,x)$ that is concave with respect to the state variable $x$ in…
Necessary and sufficient conditions are given for the existence of solutions to the discrete Lp Minkowski problem for the critical case where 0 < p < 1.
We study the critical points of the solution of second elliptic equations in divergence and diagonal form with a bounded and positive definite coefficient, under the assumption that the statement of the Hopf lemma holds (sign assumptions on…