Related papers: Multiple return times in the quantum baker map
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201…
We study returns in dynamical systems: when a set of points, initially populating a prescribed region, swarms around phase space according to a deterministic rule of motion, we say that the return of the set occurs at the earliest moment…
We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the…
The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…
We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic…
The correspondence principle plays an important role in understanding the emergence of classical chaos from an underlying quantum mechanics. Here we present an infinite family of quantum dynamics that never resembles the analogous classical…
Randomly repeated measurements during the evolution of a closed quantum system create a sequence of probabilities for the first detection of a certain quantum state. The related discrete monitored evolution for the return of the quantum…
Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition…
Long periodic orbits constitute a serious drawback in Gutzwiller's theory of chaotic systems, and then it would be desirable that other classical invariants, not suffering from the same problem, could be used in the quantization of such…
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos,…
Transfer operators have been used widely to study the long time properties of chaotic maps or flows. We describe quantum analogues of these operators, which have been used as toy models by the quantum chaos community, but are also relevant…
Quantum chaos plays a significant role in understanding several important questions of recent theoretical and experimental studies. Here, by focusing on the localization properties of eigenstates in phase space (by means of Husimi…
We quantise and study several versions of finite multibaker maps. Classically these are exactly solvable K-systems with known exponential decay to global equilibrium. This is an attempt to construct simple models of relaxation in quantum…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the…
We show that quantum effects modify the decay rate of Poincar\'e recurrences P(t) in classical chaotic systems with hierarchical structure of phase space. The exponent p of the algebraic decay P(t) ~ 1/t^p is shown to have the universal…
In this work we make use of generalized inverses associated with quantum channels acting on finite-dimensional Hilbert spaces, so that one may calculate the mean hitting time for a particle to reach a chosen goal subspace. The questions…
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with…
We investigate recurrence phenomena in coupled two degrees of freedom systems. It is shown that an initial well localized wave packet displays recurrences even in the presence of coupling in these systems. We discuss the interdependence of…