Related papers: Two dimensional periodic box-ball system and its f…
We study the statistical properties of two hard spheres in a two dimensional rectangular box. In this system, the relation like Van der Waals equation loop is obtained between the width of the box and the pressure working on side walls. The…
Approximate but reliable solutions of a quantum system with $N$ identical particles can be easily computed with the envelope theory, also known as the auxiliary field method. This technique has been developed for Hamiltonians with arbitrary…
In the present note, we uncover a remarkable connection between the length of periodic orbit of a classical particle enclosed in a class of 2-dimensional planar billiards and the energy of a quantum particle confined to move in an identical…
Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer…
We apply periodic orbit theory to a two-dimensional non-integrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing…
Box-ball system (BBS) is a prominent example of integrable cellular automata in one dimension connected to quantum groups, Bethe ansatz, ultradiscretization, tropical geometry and so forth. In this paper we study the generalized Gibbs…
Phase behaviors of two-dimensional (2D) systems constitute a fundamental topic in condensed matter and statistical physics. Although hard polygons and interactive point-like particles are well studied, the phase behaviors of more realistic…
Periodic normal forms for the codim 2 bifurcations of limit cycles up to a 3-dimensional center manifold in generic autonomous ODEs and computational formulas for their coefficients are derived. The formulas are independent of the dimension…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with…
We investigate the Brusselator system with diffusion and Dirichlet boundary conditions on one dimensional space interval. Our proof demonstrates that, for certain parameter values, a periodic orbit exists. This proof is computer-assisted…
We investigate the dynamics of Q-balls in one, two and three space dimensions, using numerical simulations of the full nonlinear equations of motion. We find that the dynamics of Q-balls is extremely complex, involving processes such as…
Periodic orbit theory for classical hyperbolic system is very significant matter of how we can interpret spectral statistics in terms of semiclassical theory. Although pruning is significant and generic property for almost all hyperbolic…
In this paper we explicate a method of quantum hydrodynamics (QHD) for the study of the quantum evolution of a system of polarized particles. Though we focused primarily on the two-dimension physical systems, the method is valid for…
This paper is devoted to study the limit cycle problem of a cubic reversible system with an isochronous center, when it is perturbed inside a class of polynomials. An upper bound of the number of limit cycles is obtained using the Abelian…
Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a…
In order to better understand the structure of quantum theory, or speculate about theories that may supercede it, it can be helpful to consider alternative physical theories. ``Boxworld'' describes one such theory, in which all…
We apply periodic-orbit theory to calculate the integrated density of states $N(k)$ from the periodic orbits of pseudointegrable polygon and barrier billiards. We show that the results agree so well with the results obtained from direct…
We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…