Related papers: Classical and quantum billiard inside the square w…

We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory…

In this paper, we explore two different ways of implementing quantum effects in a classical structure. The first one is through an external field. The other one is modifying the classical conservation laws. In both cases, the consequences…

Quantized space described by time reversal invariant and rotationally invariant noncommutative algebra of canonical type is studied. A particle in uniform field is considered. We find exactly the energy of a particle in uniform field in the…

We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…

We investigate a multi-player and multi-choice quantum game. We start from two-player and two-choice game and the result is better than its classical version. Then we extend it to N-player and N-choice cases. In the quantum domain, we…

We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…

This article traces a brief history of the use of single electron spins to compute. In classical computing schemes, a binary bit is represented by the spin polarization of a single electron confined in a quantum dot. If a weak magnetic…

We consider the free motion of a point particle inside a circular billiard with periodically moving boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the energy of the particle is not…

Sufficiently differentiable oval billiards always have invariant rotational curves, but there are only two types of ovals with an invariant horizontal circle in its phase-space: the constant width ovals and some very special symmetric…

These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black…

In classical physics, there is a basic principle, namely "A particle cannot be located at the position of another one on the same time". Which consequences can be derived if this principle is transferred into quantum physics? For doing…

In this paper we are interested in the motion of a ball inside a billiard table bounded by a particular smooth curve. This table belongs to a family of billiards which can all be drawn by a common process: the so-called gardener's string…

We study combinatorics of billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in d-dimensional Euclidean and pseudo-Euclidean spaces. Such partitions uniquely codify the sets of…

Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…

I reconsider Hawking's analysis of the effects of gravitational collapse on quantum fields, taking into account interactions between the fields. The ultra-high energy vacuum fluctuations, which had been considered to be an awkward…

Dynamical properties of the elliptical stadium billiard, which is a generalization of the stadium billiard and a special case of the recently introduced mushroom billiards, are investigated analytically and numerically. In dependence on two…

This paper examines the variance of quantum and classical predictions in the quantum realm, as well as unexpected presence and absence of variances. Some features are found that share an indirect commonality with the Aharonov-Bohm and…

A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…

Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of…

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…