Related papers: Propagation of Correlations in Quantum Lattice Sys…
We study the velocity of the propagation of information for a class of local dissipative quantum dynamics. This finite velocity is expressed by the so-called Lieb-Robinson bound. Besides the properties of the already studied dynamics, we…
We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
We give an overview of recent results on Lieb-Robinson bounds and some of their applications in the study of quantum many-body models in condensed matter physics.
This paper gives the first full proof of the justification of the linear Boltzmann equation from an underlying long range particle evolution. We suppose that a tagged particle is interacting with a background via a two body potential that…
In this paper we consider the hyperbolic-elliptic system of two conservation laws that describes the dynamics of an elastic material governed by a non-monotone strain-stress function. Following Abeyaratne and Knowles, we propose a notion of…
We propose a mechanism for liquid formation in strongly correlated lattice systems. The mechanism is based on an interplay between long-range attraction and superexchange processes. As an example, we study dipolar bosons in one-dimensional…
Long-range quantum lattice systems often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent…
We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction…
The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is…
We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple…
We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect it's arrival at a particular chosen set of sites. The projective measurements are made at regular time…
We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by…
For an interacting system of N electrons, we study the conditions under which a lattice model of size L with nearest neighbor hopping t and U/r Coulomb repulsion has the same ground state as a continuum model. For a fixed value of N, one…
In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently…
Using the information content of correlations between multipartite systems, together with the notion of partitioning, we show that some general results about the evolution of correlations in quantum systems can be derived with only…
The aim of this paper is to compare results from lattice-Boltzmann and Brownian dynamics simulations of linear chain molecules. We have systematically varied the parameters that may affect the accuracy of the lattice-Boltzmann simulations,…
We show that in a gas of ultra cold atoms distance selective two-body loss can be engineered via the resonant laser excitation of atom pairs to interacting electronic states. In an optical lattice this leads to a dissipative Master equation…
We prove global existence and uniqueness of dynamics on the quasi-local algebra $\mathcal{A}$ of a quantum lattice system for spatially growing derivations $\mathcal{L}_\Phi = \sum_x [ \Phi_x , \cdot ]$. Existing results assume that the…
We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same procedure to higher dimensions using ideas…