Classical intermittency and quantum Anderson transition

We investigate the quantum properties of 1D quantum systems whose classical counterpart presents intermittency. The spectral correlations are expressed in terms of the eigenvalues of an anomalous diffusion operator by using recent semiclassical techniques. For certain values of the parameters the spectral properties of our model show similarities with those of a disordered system at the Anderson transition. In Hamiltonian systems, intermittency is closely related to the presence of cantori in the classical phase space. We suggest, based on this relation, that our findings may be relevant for the description of the spectral correlations of (non-KAM) Hamiltonians with a classical phase space filled by cantori. Finally we discuss the extension of our results to higher dimensions and their relation to Anderson models with long range hopping.Comment: 4 pages, typos corrected, references adde

Classical and quantum anomalous diffusion in a system of 2δ\delta-kicked Quantum Rotors

We study the dynamics of cold atoms subjected to {\em pairs} of closely time-spaced $\delta$-kicks from standing waves of light. The classical phase space of this system is partitioned into momentum cells separated by trapping regions. In a certain range of parameters it is shown that the classical motion is well described by a process of anomalous diffusion. We investigate in detail the impact of the underlying classical anomalous diffusion on the quantum dynamics with special emphasis on the phenomenon of dynamical localization. Based on the study of the quantum density of probability, its second moment and the return probability we identify a region of weak dynamical localization where the quantum diffusion is still anomalous but the diffusion rate is slower than in the classical case. Moreover we examine how other relevant time scales such as the quantum-classical breaking time or the one related to the beginning of full dynamical localization are modified by the classical anomalous diffusion. Finally we discuss the relevance of our results for the understanding of the role of classical cantori in quantum mechanics.Comment: 9 pages, 3 figure

The QCD vacuum as a disordered medium: A simplified model for the QCD Dirac operator

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the (dimensionless) Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling of the (dimensionless) Thouless energy in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.Comment: 4 pages, 3 figure