160,331 research outputs found
Classical and quantum anomalous diffusion in a system of 2-kicked Quantum Rotors
We study the dynamics of cold atoms subjected to {\em pairs} of closely
time-spaced -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
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