Related papers: Quantum wave packet revivals in circular billiards
We investigate a circular cavity billiard within which a pair of identical hard disks of smaller but finite size is confined. Each disk shows a free motion except when bouncing elastically with its partner and with the boundary wall.…
Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum…
The paper deals with the semi-classical behaviour of quantum dynamics for a semi-classical completely integrable system with two degrees of freedom near Liouville regular torus. The phenomomenon of wave packet revivals is demonstrated in…
The emergence of power laws that govern the large-time dynamics of a one-dimensional billiard of $N$ point particles is analysed. In the initial state, the resting particles are placed in the positive half-line $x\geqslant 0$ at equal…
We report fractional revival phenomena in an ultracold matter wave inside a ring waveguide. The specific fractional revival times are precisely identified and corresponding spatial density patterns are depicted. Thorough analyses of the…
In this paper we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a 2-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism,…
Nonperiodic tunable quantum echoes have been observed in experiments with an open microwave billiard whose geometry under certain conditions provides Fibonacci like sequences of classical delay times. These sequences combined with the…
In a quantum revival, a localized wavepacket re-forms or "revives" into a compact reincarnation of itself long after it has spread in an unruly fashion over a region restricted only by the potential energy. This is a purely quantum…
The conception of almost complete revivals has been introduced recently. In a quantum many-body system local observable may exhibit an almost complete revival to its maximal value at the predetermined moment of time. In this paper we extend…
The first two period behaviors of a quantum wave packet in an infinite square well potential is studied. First, the short term behavior of expectation value of a quantity on an equally weighted wave packet (EWWP) is in classical limit…
A simple relation is developed between elastic collisions of freely-moving point particles in one dimension and a corresponding billiard system. For two particles with masses m_1 and m_2 on the half-line x>0 that approach an elastic barrier…
We analyze the time evolution of simple nuclear rotational wave packets (WP) called circular, linear or elliptic, depending on squeezing parameter $\eta$, assuming that $E=\hbar\omega_0 I(I+1)$. The scenario of fractional revivals found by…
In this paper we discuss some aspects of the theory of wave packets. We consider a popular non-covariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic…
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…
The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…
We derive an exact analytical solution to the time-dependent Schr\"odinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet…
Time evolution of radial wave packets built from the eigenstates of Dirac equation for a hydrogenic systems is considered. Radial wave packets are constructed from the states of different $n$ quantum number and the same lowest angular…
A class of truncated tight-binding Hermitian and non-Hermitian lattices with commensurate energy levels, showing periodic reconstruction of the wave packet, is presented. Examples include exact Bloch oscillations on a finite lattice,…
The time evolution of a particle, caught in an infinitely deep square well, displays unexpected features, when one includes tiny relativistic effects. Indeed, even the smallest corrections to the non-relativistic quadratic spectrum manifest…
We test the ability of semiclassical theory to describe quantitatively the revival of quantum wavepackets --a long time phenomena-- in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are…