Related papers: Assisted exchange models in one dimension
Quantum link models are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. Quantum link models not only reproduce the standard features of Wilson's lattice gauge…
We construct a class of assisted hopping models in one dimension in which a particle can move only if it does not lie in an otherwise empty interval of length greater than $n+1$. We determine the exact steady state by a mapping to a gas of…
We present a convenient and efficient way to exchange and distribute multipartite entangled state via atomic coherence induced by electromagnetically induced transparency (EIT) in an atomic ensemble. By using the EIT-based nondegenerate…
In reconstituting k-mer models, extended objects which occupy several sites on a one dimensional lattice, undergo directed or undirected diffusion, and reconstitute -when in contact- by transferring a single monomer unit from one k-mer to…
We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…
We study the steady-state behavior of a driven non-equilibrium lattice gas of hard-core particles with next-nearest-neighbor interaction. We calculate the exact stationary distribution of the periodic system and for a particular line in the…
Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…
We consider a model of boosted dark matter (DM), where a fraction of DM is upscattered to relativistic energies by cosmic ray electrons. Such interactions responsible for boosting the DM also attenuate its flux at the Earth. Considering a…
Cooperative ring-exchange is suggested as a mechanism of quantum melting of vortex lattices in a rapidly-rotating quasi two dimensional atomic Bose-Einstein condensate (BEC). Using an approach pioneered by Kivelson et al. [Phys. Rev. Lett.…
I propose a model of mutually interacting particles on an M-dimensional unit sphere. I derive the dynamics of the particles by extending the dynamics of the Kuramoto-Sakaguchi model. The dynamics include a natural-frequency matrix, which…
The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy.…
We formulate a new atomistic/continuum (a/c) coupling scheme that employs the boundary element method (BEM) to obtain an improved far-field boundary condition. We establish sharp error bounds in a 2D model problem for a point defect…
We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field; the interaction operates only between particles belonging to different species. After an…
In this study, we leverage a mixture model learning approach to identify defects in laser-based Additive Manufacturing (AM) processes. By incorporating physics based principles, we also ensure that the model is sensitive to meaningful…
Accurate modeling in the warm dense matter regime is a persistent challenge with the most detailed models such as quantum molecular dynamics and path integral Monte Carlo being immensely computationally expensive. Density functional theory…
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…
We consider a model of weakly coupled quantum Ising chains. We describe the phase diagram of such a model and study the dynamical magnetic susceptibility by means of Bethe ansatz and the Random Phase Approximation applied to the inter-chain…
In this thesis, we consider one of the most popular models of non-equilibrium statistical physics: the Asymmetric Simple Exclusion Process, in which particles jump stochastically on a one-dimensional lattice, between two reservoirs at fixed…
We consider the collective behaviour of active particles that locally align with their neighbours. Agent-based simulation models have previously shown that in one dimension, these particles can form into a flock that maintains its stability…