相关论文: A Graphical User Interface to Simulate Classical B…

We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…

We prove some partial results on the periodicity of billiard systems on graphs. The results specialize to the case of $n$ billiards with equal mass on the unit interval or circle traveling at the same speed.

A widely used mathematical model for the bouncing motion of an ideally elastic ball -- referred to in previous work by the first two authors and collaborators as a {\em no-slip billiard} system -- exhibits some notable dynamical behavior…

We report on the numerical simulation of the double-slit experiment, where the initial wave-packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is…

In a recent preprint [1] (arXiv:2503.05693), Tindall et al. presented impressive classical simulations of quantum dynamics using tensor networks. Their methods represent a significant improvement in the classical state of the art, and in…

We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schroedinger equation with energy rescaled by the billiard dimension. As…

We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of…

Recent developments in Machine Learning approaches for modelling physical systems have begun to mirror the past development of numerical methods in the computational sciences. In this survey, we begin by providing an example of this with…

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…

We study the thermal rectification phenomenon in ``billiard'' systems with interacting particles. This interaction induces a local dynamical response of the billiard to an external thermodynamic gradient. To explain this dynamical effect we…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

We introduce a new class of billiard-like system, ``bouncing outer billiards" which are 3-dimensional cousins of outer billiards of Neumann and Moser. We prove that bouncing outer billiard on a smooth convex body has at least four…

In this paper, we extend the scope of symbolic dynamics to encompass a specific class of ideal polyhedrons in the 3-dimensional hyperbolic space, marking an important step forward in the exploration of dynamical systems in non-Euclidean…

We demonstrate that the free motion of any two-dimensional rigid body colliding elastically with two parallel, flat walls is equivalent to a billiard system. Using this equivalence, we analyze the integrable and chaotic properties of this…

In this work, we introduce a novel concept of magic billiards, which can be seen as an umbrella, unifying several well-known generalisations of mathematical billiards. We analyse properties of magic billiards in the case of elliptical…

A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary,…

In this article we introduce a simple dynamical system called symplectic billiards. As opposed to usual/Birkhoff billiards, where length is the generating function, for symplectic billiards symplectic area is the generating function. We…

The role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures. We find that an otherwise simple…

The exact and semiclassical quantum mechanics of the elliptic billiard is investigated. The classical system is integrable and exhibits a separatrix, dividing the phasespace into regions of oscillatory and rotational motion. The classical…

This article is intended for physics educators and students at school and undergraduate level. It is used at our department to introduce students to simulation and offer a guide in using statistics in physics. The simulation code was…