Related papers: Multiple return times in the quantum baker map

The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…

Quantum baker`s map is a model of chaotic system. We study quantum dynamics for the quantum baker's map. We use the Schack and Caves symbolic description of the quantum baker`s map. We find an exact expression for the expectation value of…

We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a…

We introduce and study the classical and quantum mechanics of certain non hyperbolic maps on the unit square. These maps are modifications of the usual baker's map and their behaviour ranges from chaotic motion on the whole measure to chaos…

Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincar\'{e} recurrences for a rotation map: only three distinct…

We define a class of dynamical systems on the sphere analogous to the baker map on the torus. The classical maps are characterized by dynamical entropy equal to ln 2. We construct and investigate a family of the corresponding quantum maps.…

We study the quantum mechanics of a generalized version of the baker's map. We show that the Ruelle resonances (which govern the approach to ergodicity of classical distributions on phase space) also appear in the quantum correlation…

A method for the semiclassical quantization of chaotic maps is proposed, which is based on harmonic inversion. The power of the technique is demonstrated for the baker's map as a prototype example of a chaotic map.

The characteristic stretching and squeezing of chaotic motion is linearized within the finite number of phase space domains which subdivide a classical baker map. Tensor products of such maps are also chaotic, but a more interesting…

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way I prove versions of the recurrence…

We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special…

The classical Bernoulli and baker maps are two simple models of deterministic chaos. On the level of ensembles, it has been shown that the time evolution operator for these maps admits generalized spectral representations in terms of…

By studying a modified (unbiased) quantum multibaker map, we were able to obtain a {\em finite} asymptotic quantum current without a classical analogue. This result suggests a general method for the design of {\em purely} quantum ratchets,…

A set of quantum states, dynamically related to the classical periodic orbits of a chaotic map, is used as a basis in which the description of the eigenstates of its quantum version is greatly simplified. This set can be improved with the…

Many quantum systems may have the same classical limit. We argue that in the classical limit their traces do not necessarily converge one to another. The trace formula allows to express quantum traces by means of classical quantities as…

We propose a generalization of the model of classical baker map on the torus, in which the images of two parts of the phase space do overlap. This transformation is irreversible and cannot be quantized by means of a unitary Floquet…

We investigate the quantum recurrence phenomena in periodically driven systems. We calculate the classical period and the quantum recurrence time and develop their interdependence. We further predict the behavior of the recurrence phenomena…

We study the distribution of overlaps with the computational basis of a quantum state generated under generic quantum many-body chaotic dynamics, without conserved quantities, for a finite time $t$. We argue that, scaling time…

This paper reports on the experimental implementation of the quantum baker's map via a three bit nuclear magnetic resonance (NMR) quantum information processor. The experiments tested the sensitivity of the quantum chaotic map to…

Quantum kicked top is a fundamental model for time-dependent, chaotic Hamiltonian system and has been realized in experiments as well. As the quantum kicked top can be represented as a system of qubits, it is also popular as a testbed for…