相关论文: Describing a Universal Critical Behavior in a tran…

We study billiards in domains enclosed by circular polygons. These are closed $C^1$ strictly convex curves formed by finitely many circular arcs. We prove the existence of a set in phase space, corresponding to generic sliding trajectories…

In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through…

The spontaneous breaking of non-invertible symmetries can lead to exotic phenomena such as coexistence of order and disorder. Here we explore second-order phase transitions in 1d spin chains between two phases that correspond to distinct…

Nonequlibrium phase transition of an open Takayama-Lin Liu-Maki chain coupled with two reservoirs is investigated by combining a mean-field approximation and a formula characterizing nonequlibrium steady states, which is obtained from the…

This work explores a deformation of the Kitaev toric code that induces a phase transition out of the topologically ordered phase. By placing the model on a cylinder, the bulk global 1-form symmetries separate into distinct boundary…

We study the dynamical properties of a particle in a non-planar square billiard. The plane of the billiard has a sinusoidal shape. We consider both the static and time-dependent plane. We study the affect of different parameters that…

A class of Hamiltonian impact systems exhibiting smooth near integrable behavior is presented. The underlying unperturbed model investigated is an integrable, separable, 2 degrees of freedom mechanical impact system with effectively bounded…

The transition from complex-periodic to chaotic behavior is investigated in oscillatory media supporting spiral waves. We find turbulent regimes characterized by the spontaneous nucleation, proliferation and erratic motion of…

We describe non-equilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or…

We present a field theoretic renormalization group study for the critical behaviour of a uniformly driven diffusive system with quenched disorder, which is modelled by different kinds of potential barriers between sites. Due to their…

Failure in disordered solids is accompanied by intermittent fluctuations extending over a broad range of scales. The implied scaling has been previously associated with either spinodal or critical points. We use an analytically transparent…

The behavior of homogeneous and disordered systems with a free boundary is described on the basis of group theory in the two-loop approximation directly in three-dimensional space. The effect of the free boundary on the regime of the bulk…

On the phase diagram of a system undergoing a continuous phase transition of the second order, three lines, hyper-surfaces, convergent into the critical point feature prominently: the ordered and disordered phases in the thermodynamic…

We study a continuous quasi-two-dimensional order-disorder phase transition that occurs in a simple model of a material that is inhomogeneously strained due to the presence of dislocation lines. Performing Monte Carlo simulations of…

We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…

We present a dynamical analysis of a classical billiard chain -- a channel with parallel semi-circular walls, which can serve as a model for a bended optical fiber. An interesting feature of this model is the fact that the phase space…

The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space Among different indicators signaling this behavior, the study of the long-time…

We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…

We investigate statistical properties of several classes of periodic billiard models which are diffusive. An introductory chapter gives motivation, and then a review of statistical properties of dynamical systems is given in chapter 2. In…

We study some new universal aspects of diffusion in chaotic systems, especially such having very large Lyapunov coefficients on the chaotic (indecomposable, topologically transitive) component. We do this by discretizing the chaotic…