Related papers: Dynamical Stochastic Higher Spin Vertex Models

We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…

We show that the anisotropic Heisenberg-Ising chains with higher spin allow, for special values of the anisotropy, integrable deformations intimately related to the theory of quantum groups at roots of unity. For the spin one case we…

The main result of this paper is that there are examples of stochastic partial differential equations [hereforth, SPDEs] of the type $$ \partial_t u=\frac12\Delta u +\sigma(u)\eta \qquad\text{on $(0\,,\infty)\times\mathbb{R}^3$}$$ such that…

We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties.…

We consider quantum-dynamical phenomena in the $\mathrm{SU}(2)$, $S=1/2$ infinite-range quantum Heisenberg spin glass. For a fermionic generalization of the model we formulate generic dynamical self-consistency equations. Using the…

We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical…

We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an alternative…

The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…

We present a new derivation of Israel-Stewart-like relativistic second-order dissipative spin hydrodynamic equations using the entropy current approach. In our analysis, we consider a general energy-momentum tensor with symmetric and…

We resolve the real-time dynamics of a purely dissipative $s = 1/2$ quantum spin or, equivalently, hard-core boson model on a hypercubic $d$-dimensional lattice. The considered quantum dissipative process drives the system to a totally…

Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a…

We develop here a stochastic framework for modeling and segmenting transient spindle-like oscillatory bursts in electroencephalogram (EEG) signals. At the modeling level, individual spindles are represented as path realizations of a…

We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…

We analyze a modified version of the Coleman-Hepp model, that is able to take into account energy-exchange processes between the incoming particle and the linear array made up of $N$ spin-1/2 systems. We bring to light the presence of a…

An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…

This paper presents a rigorous mathematical analysis, alongside simulation studies, of a spatially extended stochastic electrophysiology model, the Hodgkin-Huxley model of the squid giant axon being a classical example. Although most…

We revisit the out-of-equilibrium physics arising during the unitary evolution of a one-dimensional XXZ spin chain initially prepared in a domain wall state $\vert\psi_0\rangle=\vert\dots \uparrow\uparrow\downarrow\downarrow\dots\rangle$.…

We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…

The branching rule for spin irreducible representations of symmetric groups gives rise to a Markov chain on the spin dual $(\widetilde{\mathfrak{S}}_n)^\wedge_{\mathrm{spin}}$ of symmetric group $\mathfrak{S}_n$ through restriction and…

We study the symmetric Dyson exclusion process (SDEP) - a lattice gas with exclusion and long-range, Coulomb-type interactions that emerge both as the maximal-activity limit of the symmetric exclusion process and as a discrete version of…