Related papers: Thermodynamic Limit and Dispersive Regularisation …
Density-matrix topology, defined through the geometric property of the relevant modular Hamiltonian, can undergo transitions in the corresponding open-system dynamics. While symmetry considerations are crucial to ensure such a dynamic…
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…
Understanding the realization of thermal equilibrium through the thermalization process in a many-body system is a fundamental and complex scientific question, bridging thermodynamics and classical dynamics and connecting to a host of…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
Thermodynamic computing exploits fluctuations and dissipation in physical systems to efficiently solve various mathematical problems. For example, it was recently shown that certain linear algebra problems can be solved thermodynamically,…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
In this Rapid Research Note the application of recently introduced [Physica A 277 (2000) 157] entropic measure S_Delta of spatial disorder for systems of finite-sized objects is presented. In the thermodynamic limit the critical behaviour…
We describe how to implement the time-dependent variational principle for matrix product states in the thermodynamic limit for nonuniform lattice systems. This is achieved by confining the nonuniformity to a (dynamically growable) finite…
How can a system in a macroscopically stable state explore energetically more favorable states, which are far away from the current equilibrium state? Based on continuum mechanical considerations we derive a Boussinesq-type equation which…
The paper is devoted to a study of phase transitions in the Hermitian random matrix models with a polynomial potential. In an alternative equivalent language, we study families of equilibrium measures on the real line in a polynomial…
We investigate a two-dimensional tiling model. Even though the degrees of freedom in this model are discrete, it has a hidden continuous global symmetry in the infinite lattice limit, whose corresponding Goldstone modes are the…
We consider a system of N point particles moving on a d-dimensional torus. Each particle is subject to a uniform field E and random speed conserving collisions. This model is a variant of the Drude-Lorentz model of electrical conduction. In…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…
We study dynamics of a membrane and its matrix regularisation. We present the matrix regularisation for a membrane propagating in a curved space-time geometry in the presence of an arbitrary 3-form field. In the matrix regularisation, we…
We study thermodynamical properties of a fuzzy sphere in matrix quantum mechanics of the BFSS type including the Chern-Simons term. Various quantities are calculated to all orders in perturbation theory exploiting the one-loop saturation of…
Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…
The conditions of multi-phase equilibrium are solved for generic polydisperse systems. The case of multiple polydispersity is treated, where several properties (e.g. size, charge, shape) simultaneously vary from one particle to another. By…
We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent…
Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Such "rotors" are found in the natural world spanning vastly disparate length scales - from the rotor proteins…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…