Related papers: Leaking Chaotic Systems
In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…
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…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which…
We introduce the notion of a leak for general process theories, and identify quantum theory as a theory with minimal leakage, while classical theory has maximal leakage. We provide a construction that adjoins leaks to theories, an instance…
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 obtain a description of the Poincar\'e recurrences of chaotic systems in terms of the ergodic theory of transient chaos. It is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by…
Mesoscopic devices, with system sizes in the range of several to several dozens wavelengths, represent paradigmatic model systems for the observation of quantum chaotic behaviour based on semiclassical concepts. Those electronic and…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
We study the dielectric annular billiard as a quantum chaotic model of a micro-optical resonator. It differs from conventional billiards with hard-wall boundary conditions in that it is partially open and composed of two dielectric media…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
Hamiltonian systems that are either open, leaking, or contain holes in the phase space possess solutions that eventually escape the system's domain. The motion described by such escape orbits before crossing the escape threshold can be…
We study analytically and numerically the classical diffusive process which takes place in a chaotic billiard. This allows to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described…
A family of the billiard-type systems with zero Lyapunov exponent is considered as an example of dynamics which is between the regular one and chaotic mixing. This type of dynamics is called ``pseudochaos''. We demonstrate how the…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex…