Article
Critical state of the Anderson transition: between a metal and an insulator.
Laboratoire Kastler Brossel, UPMCParis 6, ENS, CNRS; 4 Place Jussieu, F75005 Paris, France.
Physical Review Letters (Impact Factor: 7.73). 08/2010; 105(9):090601. DOI: 10.1103/PHYSREVLETT.105.090601 Source: arXiv

Article: Exponential quantum spreading in a class of kicked rotor systems near highorder resonances.
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ABSTRACT: Longlasting exponential quantum spreading was recently found in a simple but very rich dynamical model, namely, an onresonance doublekicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasiintegrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain longlasting exponential quantum spreading under much more general conditions. In particular, we adopt the socalled "spinor" representation to treat the kickedrotor dynamics under highorder resonance conditions and then exploit the BornOppenheimer approximation to understand the dynamical evolution. It is found that the existence of a flat band (or an effectively flat band) is one important feature behind why and how the exponential dynamics emerges. It is also found that a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate. In addition to general interests regarding the question of how exponential behavior in quantum systems may persist for a long time scale, our results should motivate further studies toward a better understanding of highorder resonance behavior in δkicked quantum systems.Physical Review E 11/2013; 88(51):052919. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Starting from a microscopic theory for atomic scatterers, we describe the scattering of light by a single atom and study the coherent propagation of light in a cold atomic cloud in the presence of a magnetic field B in the mesoscopic regime. Nonpertubative expressions in B are given for the magnetooptical effects and optical anisotropy. We then consider the multiplescattering regime and address the fate of the coherentbackscattering (CBS) effect. We show that, for atoms with nonzero spin in their ground state, the CBS interference contrast can be increased compared to its value when B=0, a result at variance with classical samples. We validate our theoretical results by a quantitative comparison with experimental data.Physical Review A 09/2013; 88(3). · 3.04 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Recent studies have established that, in addition to the wellknown kickedHarper model (KHM), an onresonance doublekicked rotor (ORDKR) model also has Hofstadter's butterfly Floquet spectrum, with strong resemblance to the standard Hofstadter spectrum that is a paradigm in studies of the integer quantum Hall effect. Earlier it was shown that the quasienergy spectra of these two dynamical models (i) can exactly overlap with each other if an effective Planck constant takes irrational multiples of 2π and (ii) will be different if the same parameter takes rational multiples of 2π. This work makes detailed comparisons between these two models, with an effective Planck constant given by 2πM/N, where M and N are coprime and odd integers. It is found that the ORDKR spectrum (with two periodic kicking sequences having the same kick strength) has one flat band and N1 nonflat bands with the largest bandwidth decaying in a power law as ∼K^{N+2}, where K is a kick strength parameter. The existence of a flat band is strictly proven and the powerlaw scaling, numerically checked for a number of cases, is also analytically proven for a threeband case. By contrast, the KHM does not have any flat band and its bandwidths scale linearly with K. This is shown to result in dramatic differences in dynamical behavior, such as transient (but extremely long) dynamical localization in ORDKR, which is absent in the KHM. Finally, we show that despite these differences, there exist simple extensions of the KHM and ORDKR model (upon introducing an additional periodic phase parameter) such that the resulting extended KHM and ORDKR model are actually topologically equivalent, i.e., they yield exactly the same Floquetband Chern numbers and display topological phase transitions at the same kick strengths. A theoretical derivation of this topological equivalence is provided. These results are also of interest to our current understanding of quantumclassical correspondence considering that the KHM and ORDKR model have exactly the same classical limit after a simple canonical transformation.Physical Review E 11/2013; 88(51):052920. · 2.31 Impact Factor
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