Related papers: Geometrization of spin systems using cycle expansi…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
Non-equilibrium states of a thermodynamic statistical system are investigated using the thermodynamic parameter of the system lifetime, first-passage time, the time before degeneration of the system under influence of fluctuations.…
We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the…
We study the longitudinal spin polarization of a relativistic fluid of massive spin-1/2 particles undergoing a boost-invariant expansion in the longitudinal direction and rotating in the transverse plane. We express the polarization vector…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…
We consider the time evolution of entanglement in a finite two dimensional transverse Ising model. The model consists of a set of 7 localized spin-1/2 particles in a two dimensional triangular lattice coupled through nearest neighbor…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
We propose a systematic way to investigate the low-temperature thermodynamic properties of quantum spin systems subject to the restriction that only a finite number of bosons may occupy a single lattice site. Such a kinematical interaction…
The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle corresponding, in its simplest form, to the Maximum…
Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with the imperfect measurement of initial conditions. Finite-time estimates of the exponent, however,…
Cycle expansions are an efficient scheme for computing the properties of chaotic systems. When enumerating the orbits for a cycle expansion not all orbits that one would expect at first are present --- some are pruned. This pruning leads to…
Long-range spin-spin interactions are known to generate non-equilibrium dynamics which can squeeze the collective spin of a quantum spin ensemble in a scalable manner, leading to states whose metrologically useful entanglement grows with…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
It is usually expected and observed that non-integrable isolated quantum systems thermalize. However, for some non-integrable spin chain models, in a numerical study, initial states with oscillations that persisted for some time were found…
Plasma physics give an example of physical system of particles with the long range interaction. At small velocity of particles we can consider the plasma approximately as a system of particles with the Coulomb interaction. The Coulomb…
Population dynamics in systems composed of cyclically competing species has been of increasing interest recently. Here, we investigate a system with four or more species. Using mean field theory, we study in detail the trajectories in…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
Characterizing the nature of hydrodynamical transport properties in quantum dynamics provides valuable insights into the fundamental understanding of exotic non-equilibrium phases of matter. Experimentally simulating infinite-temperature…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
Spin dynamics of two-dimensional electrons in moderate in-plane electric fields is studied theoretically. The streaming regime is considered, where each electron accelerates until reaching the optical phonon energy, then it emits an optical…