We study fluctuations of survival probability in an open quantum system classically described by a map with a mixed phase space. Our results provide the first numerical support to theoretical predictions that such fluctuations have a fractal structure, quantitatively related to the algebraic decay of the classical survival probability.
We numerically analyze quantum survival probability fluctuations in an open, classically chaotic system. In a quasiclassical regime and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal pattern, on the grounds of semiclassical arguments. In contrast, we work in a classical regime of complete chaoticity and in a deep quantum regime of strong localization. We provide evidence that fluctuations are still fractal, due to the slow, purely quantum algebraic decay in time produced by dynamical localization. Such findings considerably enlarge the scope of the existing theory.
We discuss quantum relaxation and fluctuation phenomena in the light of the corresponding classical behaviour. Quantum exponential localization and tunneling effects lead to the universal algebraic decay of the survival probability P ( t ) ∝ 1/ t . This behaviour is observed in particular in the time dependence of the ionization probability of Rydberg atoms driven by a monochromatic field. At a fixed time the quantum survival probability strongly fluctuates as some parameter is varied. These fluctuations have a fractal structure which is quantitatively related to the time dependence of the survival probability.
In quantum open systems, transport coejcients such as crosssections or conductance fluctuate as functions of the relevant parameters. These fluctuations give rise to complicated patterns. An important question is their possible fractality. In this paper we present a historical review of fractal fluctuations in quantum systems and their relation to the properties of their classical counterparts. We discuss the original semiclassical predictions and various numerical and experimental results. Some numerical simulations claim explanations based on pure quantum grounds. We thus report an argument that traces fractality back to the statistical properties of the S -matrix poles. Although full understanding of the reasons for fractal fluctuations might seema secondary problem, it could lead to a deeper comprehension of quantum mechanics and its interplay with classical mechanics.
We investigate the parametric fluctuations in the quantum survival probability of an open version of the δ-kicked rotor model in the deep quantum regime. Spectral arguments (Guarneri I and Terraneo M 2001 Phys. Rev. E 65 015203(R)) predict the existence of parametric fractal fluctuations owing to the strong dynamical localization of the eigenstates of the kicked rotor. We discuss the possibility of observing such dynamically-induced fractality in the quantum survival probability as a function of the kicking period for the atom-optics realization of the kicked rotor. The influence of the atoms' initial momentum distribution is studied as well as the dependence of the expected fractal dimension on finite-size effects of the experiment, such as finite detection windows and short measurement times. Our results show that clear signatures of fractality could be observed in experiments with cold atoms subjected to periodically flashed optical lattices, which offer an excellent control on interaction times and the initial atomic ensemble.