Related papers: A quantization of interacting particle systems
Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme.…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
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…
We study the spreading of damage in the one-dimensional Ising model by means of the stochastic dynamics resulting from coupling the system and its replica by a family of algorithms that interpolate between the heat bath and the…
We consider numerically the crossover scaling behavior from the directed percolation universality class to the compact directed percolation universality class within the one-dimensional Domany-Kinzel cellular automaton. Our results are…
We construct the {\it quasi-stationary} (QS) probability distribution for the Domany-Kinzel stochastic cellular automaton (DKCA), a discrete-time Markov process with an absorbing state. QS distributions are derived at both the one- and…
We consider the exact solution of a model of correlated particles, which is presented as a system of interacting XX and Fateev-Zamolodchikov chains. This model can also be considered as a generalization of the multiband anisotropic $t-J$…
Interacting particle systems are continuous time Markov processes which are used to construct models in many disciplines. Monotonicity is a property that some interacting particle systems possess. A monotone interacting particle system is…
Motivated by recent progress in the experimental development of quantum simulators based on Rydberg atoms, we introduce and investigate the dynamics of a class of $(1+1)$-dimensional quantum cellular automata. These non-equilibrium…
We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion,…
We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions…
Interacting agent and particle systems are extensively used to model complex phenomena in science and engineering. We consider the problem of learning interaction kernels in these dynamical systems constrained to evolve on Riemannian…
We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle…
Stavskaya's model is a one-dimensional probabilistic cellular automaton (PCA) introduced in the end of the 1960's as an example of a model displaying a nonequilibrium phase transition. Although its absorbing state phase transition is well…
In this chapter we discuss methods to calculate the entanglement of a system using density-functional theory. We firstly introduce density-functional theory and the local-density approximation (LDA). We then discuss the concept of the…
Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as…
In this article, the interaction of an arbitrary number of quantum dots, behaving as artificial molecules, with different energy levels and multi-mode electromagnetic field is studied. We make the assumption that each quantum dot can be…
We develop a new density functional theory (DFT) and formalism for correlated electron systems by taking as reference an interacting electron system that has a ground state wavefunction which obeys exactly the Gutzwiller approximation for…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…