Related papers: Quantum Baker Maps for Spiraling Chaotic Motion
By analysing an n-dimensional generalisation of Thomas's cyclically symmetric attractor we find that this chaotic dynamical system behaves like a random walk constrained onto the surface of a hypersphere. The growth of error is limited,…
A generalized version of standard map is quantized as a model of quantum chaos. It is shown that, in hyperbolic chaotic regime, second moment of quantum level velocity is $\sim 1/\hbar$ as predicted by the random matrix theory.
This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic…
In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect…
We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor…
We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any…
We study the stroboscopic dynamics of a spin-$S$ object subjected to $\delta$-function kicking in the transverse magnetic field which is generated following the Fibonacci sequence. The corresponding classical Hamiltonian map is constructed…
We investigate how classical predictability of the coarse-grained evolution of the quantum baker's map depends on the character of the coarse-graining. Our analysis extends earlier work by Brun and Hartle [Phys. Rev. D 60, 123503 (1999)] to…
A model for a lattice of coupled cat maps has been recently introduced. This new and specific choice of the coupling makes the description especially easy and nontrivial quantities as Lyapunov exponents determined exactly. We studied the…
We analyze certain eigenstates of the quantum baker's map and demonstrate, using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse sequence, a simple sequence that is at the border between quasi-periodicity and chaos,…
We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for…
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…
From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal,…
For a certain parametrized family of maps on the circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit…
We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and derive a classical sum…
Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$ compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as a measure…
We have studied two complementary decoherence measures purity and fidelity for a generic diffusive noise in two different chaotic systems (the baker and the cat maps). For both quantities, we have found classical structures in quantum…
Recent experimental and theoretical studies on the magnetization dynamics driven by an electric current have uncovered a number of unprecedented rich dynamic phenomena. We predict an intrinsic chaotic dynamics that has not been previously…
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…