相关论文: Motzkin numbers out of Random Domino Automaton

If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence. Recently, Cigler and Krattenthaler showed that the…

We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on the circle. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincar\'{e} lifts) approach does depend on…

Lattice Boltzmann models are briefly introduced together with references to methods used to predict their ability for simulations of systems described by partial differential equations that are first order in time and low order in space…

We study the decomposition of free random variables in terms of their orthogonal replicas from a new perspective. First, we show that the mixed moments of orthogonal replicas with respect to the normalized linear functional $\Phi$ are…

We introduce an exact Monte Carlo approach to the statistics of discrete quantum systems which does not rely on the standard fragmentation of the imaginary time, or any small parameter. The method deals with discrete objects, kinks,…

Some formulae are given for the enumeration of certain types of dissections of the convex (n+2)-gon by non-crossing diagonals. The classical Schroeder and Motzkin numbers are addressed using a cataloguing tool, the "reversive symbol". The…

A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…

We give an infinite number of exact solutions to the 5-dimensional static Einstein equation with axial symmetry by using the inverse scattering method. The solutions are characterized by two integers representing the soliton numbers. The…

We show that the current fluctuations and nonlinear response of Markovian dynamics can be obtained from a system of polynomial equations. This offers new opportunities for analytical and numerical results. As an example, we derive new…

We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…

We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…

The family of Boltzmann distributions is used in statistical mechanics to describe the distribution of states in systems with a given temperature. We give a novel characterization of this family as the unique one satisfying independence for…

It is shown that Bernoulli numbers and tangent numbers (the derivatives of the tangent function at zero) can be obtained by means of easily defined triangles of numbers in several ways, some of them very similar to the Catalan triangle and…

Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…

Chaotic dynamics of a nonlinear oscillator is considered in the semiclassical approximation. The Loschmidt echo is calculated for a time scale which is of the power law in semiclassical parameter. It is shown that an exponential decay of…

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic…

The so-called Maryland model is a linear version of the quantum kicked rotor; it exhibits Anderson localization in momentum space. By turning the kicks into a Markovian stochastic process, the dynamics becomes a dissipative quantum process…

It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo…

The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…

The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical…