相关论文: The Integrable Snake Model
Rotating Snakes is a visual illusion in which a stationary design is perceived to move dramatically. In the current study, the mechanism that generates perception of motion was analyzed using a combination of psychophysics experiments and…
For a random walk on the integer lattice $\mathbb{Z}$ that is attracted to a strictly stable process with index $\alpha\in (1, 2)$ we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set.…
We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…
A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that…
Satisfying spin-assignments in triangulations of a surface are states of minimum energy of the antiferromagnetic Ising model on triangulations which correspond (via geometric duality) to perfect matchings in cubic bridgeless graphs. In this…
A detailed study of an $S={1\over2}$ spin ladder model is given. The ladder consists of plaquettes formed by nearest neighbor rungs with all possible SU(2)-invariant interactions. For properly chosen coupling constants, the model is shown…
We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite…
We review the recent construction \cite{brower2024isingmodelmathbbs2} of the 2d Ising model on a triangulated sphere $\mathbb{S}^2$. Surprisingly, this led to a precise map of the lattice couplings to the target geometry in order to reach…
We prove that it is NP-hard to decide whether two points in a polygonal domain with holes can be connected by a wire. This implies that finding any approximation to the shortest path for a long snake amidst polygonal obstacles is NP-hard.…
We develop a geometric representation for the ground state of the spin-1/2 quantum XXZ ferromagnetic chain in terms of suitably weighted random walks in a two-dimensional lattice. The path integral model so obtained admits a genuine…
We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core…
We present a detailed introduction of the theory of constructible sheaf complexes in the complex algebraic and analytic setting. All concepts are illustrated by many interesting examples and relevant applications, while some important…
We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the…
We study (slope-)stability properties of syzygy bundles on a projective space P^N given by ideal generators of a homogeneous primary ideal. In particular we give a combinatorial criterion for a monomial ideal to have a semistable syzygy…
We present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components along with subsets of at most three vertices into a tree. The polynomial time algorithm…
This article introduces a quantized chip-firing model with close connections to the theory of rational lattice paths and rational parking functions. Given a graph with a sink and positive integers a,b,c with gcd(a,b)=1, a set S of vertices…
Motivated by a possible convergence of terrestrial limbless locomotion strategies ultimately determined by interfacial effects, we show how both 3D gait alterations and locomotory adaptations to heterogeneous terrains can be understood…
We consider a finite one-dimensional totally asymmetric simple exclusion process (TASEP) with four types of particles, $\{1,0,\bar{1},*\}$, in contact with reservoirs. Particles of species $0$ can neither enter nor exit the lattice, and…
Generalised hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional…
We consider so-called discrete snakes obtained from size-conditioned critical Bienaym\'e-Galton-Watson trees by assigning to each node a random spatial position in such a way that the increments along each edge are i.i.d. When the offspring…