Related papers: Classical and quantum chaos in a circular billiard…
We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…
We show that deterministic quantum computing with a single bit (DQC1) can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where $N$ is the dimension of the Hilbert space of…
This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum…
The classical dynamics of the isotropic two-dimensional harmonic oscillator confined by an elliptic hard wall is discussed. The interplay between the harmonic potential with circular symmetry and the boundary with elliptical symmetry does…
The dynamics of systems composed of a classical sector plus a quantum sector is studied. We show that, even in the simplest cases, (i) the existence of a consistent canonical description for such mixed systems is incompatible with very…
This chapter provides an overview of chaotic billiard lasers as a prominent branch of quantum chaos. These lasers offer an ideal experimental platform for demonstrating the principles of quantum chaos within a physical system. We begin by…
Selection of an ensemble of equally prepared quantum systems, based on measurements on it, is a basic step in quantum state purification. For an ensemble of single qubits, iterative application of selective dynamics has been shown to lead…
We investigate the spin dynamics of a dipole-coupled system by comparing a direct solution of the Schrodinger equation for quantum spins with simulations of classical spins. Although classical spins have long been used in microscopic spin…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and against each other. In the one-particle case,…
We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…
The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced…
The relative motion of three impenetrable particles on a ring, in our case two identical fermions and one impurity, is isomorphic to a triangular quantum billiard. Depending on the ratio $\kappa$ of the impurity and fermion masses, the…
Neutrino billiards serve as a model system for the study of aspects of relativistic quantum chaos. These are relativistic quantum billiards consisting of a spin-1/2 particle which is confined to a planar domain by imposing boundary…
Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be…
Effective classicality of a property of a quantum system can be defined using redundancy of its record in the environment. This allows quantum physics to approximate the situation encountered in the classical world: The information about 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 examine the quantum motion of two particles interacting through a contact force which are confined in a rectangular domain in two and three dimensions. When there is a difference in the mass scale of two particles, adiabatic separation…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
We investigate a class of mechanical billiards, where a particle moves in a planar region under the influence of an n-centre potential and reflects elastically on a straight wall. Motivated by Boltzmann's original billiard model we explore…