Related papers: Matrix product state of multi-time correlations
We study a cellular automaton model, which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each timestep. Unit amount of energy is randomly added…
The relaxation to equilibrium of lattice systems with long-range interactions is investigated. The timescales involved depend polynomially on the system size, potentially leading to diverging equilibration times. A kinetic equation for…
Non-linearity and finite signal propagation speeds are omnipresent in nature, technologies, and real-world problems, where efficient ways of describing and predicting the effects of these elements are in high demand. Advances in engineering…
We employ the density matrix renormalization group to construct the exact time-dependent exchange correlation potential for an impurity model with an applied transport voltage. Even for short-ranged interaction we find an infinitely…
An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite 1D system; it does this by embedding sites into an approximation of the infinite ``environment'' of…
Agent-based (AB) or Cellular Automata (CA) models are rule based and are a relatively simple discrete method that can be used to simulate complex interactions of many agents or cells. The relative ease of implementing the computational…
Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
We introduce an approach to describe quantum-coherent evolution of a system of cold atoms in an optical lattice triggered by a change in superlattice potential. Using a time-dependent mean field description, we map the problem to a strong…
A set of N independent Gaussian linear time invariant systems is observed by M sensors whose task is to provide the best possible steady-state causal minimum mean square estimate of the state of the systems, in addition to minimizing a…
We investigate a chain of spinless fermions with nearest-neighbour interactions that are subject to a local loss process. We determine the time evolution of the system using matrix product state methods. We find that at intermediate times a…
The production system (multidimensional object) is considered as a dynamic system with discrete time. Formalized: space (state of the object, control actions, goals, observed values, analytical estimates). Analytical estimates of the state…
We present a general construction of matrix product states for stationary density matrices of one-dimensional quantum spin systems kept out of equilibrium through boundary Lindblad dynamics. As an application we review the isotropic…
We propose an analytic approach for the steady-state dynamics of Markov processes on locally tree-like graphs. It is based on time-translation invariant probability distributions for edge trajectories, which we encode in terms of infinite…
Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…
We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…
We explore driven lattice gases for the existence of an intensive thermodynamic variable which could determine "equilibration" between two nonequilibrium steady-state systems kept in weak contact. In simulations, we find that these systems…
A density functional theory for many-body lattice models is considered in which the single-particle density matrix is the basic variable. Eigenvalue equations are derived for solving Levy's constrained search of the interaction energy…
We define matrix product states in the continuum limit, without any reference to an underlying lattice parameter. This allows to extend the density matrix renormalization group and variational matrix product state formalism to quantum field…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…