相关论文: Dynamics and Lieb-Robinson estimates for lattices …
Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature…
We study the gap solitons and nonlinear Bloch waves of interacting bosons in one-dimensional optical lattices, taking into account the interaction from the weak to the strong limits. It is shown that composition relation between the gap…
We review some recent results on eigenvalues of fractional Laplacians and fractional Schr\"odinger operators. We discuss, in particular, Lieb-Thirring inequalities and their generalizations, as well as semi-classical asymptotics.
We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb-Liniger model, within an arbitrary eigenstate with a small particle density ${\cal D}$. They are valid for all space and time and any…
For a mixture of interacting Bose gases initially prepared in a regime of condensation (uncorrelation), it is proved that in the course of the the time evolution observables of disjoint sets of particles of each species have correlation…
We present an application of the standard Langevin dynamics to the problem of weak coupling perturbative expansions for Lattice QCD. This method can be applied to the computation of the most general observables. In this preliminary work we…
Starting from an extension of the Poisson bracket structure and Kubo-Martin-Schwinger-property of classical statistical mechanics of continuous systems to spin systems, defined on a lattice, we derive a series of, as we think, new and…
In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dynamical system as an infinite-dimensional fast-slow…
Recently, an {\it algebraic-dynamical theory} (ADT) for strongly interacting many-body quantum Hamiltonians in W. Ding, arXiv: 2202.12082 (2022). By introducing the complete operator basis set, ADT proposes a generic framework for…
We investigate a rotated, orthogonal gravitational wedge billiard - a special case of the asymmetric wedge billiard - in which the dynamics are integrable. We derive equations and conditions under which periodic orbits may be constructed…
The physics of the attractive one-dimensional Bose gas (Lieb-Liniger model) is investigated with techniques based on the integrability of the system. Combining a knowledge of particle quasi-momenta to exponential precision in the system…
The present work reports on the dynamical measures of order, disorder and complexity for the interacting bosons in optical lattice. We report results both for the relaxed state as well as quench dynamics. Our key observations are: (1)…
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
We assume one site measures without a boundary $e^{-\phi(x)}dx/Z$ that satisfy a log-Sobolev inequality. We prove that if these measures are perturbed with quadratic interactions, then the associated infinite dimensional Gibbs measure on…
We consider two linearly coupled masses, where one mass can have inelastic impacts with a fixed, rigid stop. This leads to the study of a two degree of freedom, piecewise linear, frictionless, unforced, constrained mechanical system. The…
A convenient algebraic structure to describe some forms of dynamics of two hamiltonian systems with nonpotential (magnetic--type) interaction is considered. An algebraic mechanism of generation of such dynamics is explored on simple "toy"…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that…
We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…
We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum,…
We study finite two dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape. We show that such systems can be quantum simulated by…