Article

# Critical state of the Anderson transition: between a metal and an insulator.

Laboratoire Kastler Brossel, UPMC-Paris 6, ENS, CNRS; 4 Place Jussieu, F-75005 Paris, France.

Physical Review Letters (Impact Factor: 7.73). 08/2010; 105(9):090601. DOI: 10.1103/PHYSREVLETT.105.090601 Source: arXiv

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**ABSTRACT:**We study the interplay between disorder, interactions and decoherence induced by spontaneous emission process. Interactions are included in the Anderson model via a mean-field approximation, and a simple model for spontaneous emission is introduced. Numerical simulations allow us to study the effects of decoherence on different dynamical regimes. Physical pictures for the mechanisms at play are discussed and provide simple interpretations. Finally, we discuss the validity of scaling laws on the initial state width.The European Physical Journal Special Topics 09/2012; 217(1). · 1.80 Impact Factor -
##### Article: Spectral description of the dynamics of ultracold interacting bosons in disordered lattices

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**ABSTRACT:**We study the dynamics of a nonlinear one-dimensional disordered system from a spectral point of view. The spectral entropy and the Lyapunov exponent are extracted from the short time dynamics, and shown to give a pertinent characterization of the different dynamical regimes. The chaotic and self-trapped regimes are governed by log-normal laws whose origin is traced to the exponential shape of the eigenstates of the linear problem. These quantities satisfy scaling laws depending on the initial state and explain the system behaviour at longer times.New Journal of Physics 12/2012; 15(4). · 4.06 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We realize experimentally a cold-atom system, the quasiperiodic kicked rotor, equivalent to the three-dimensional Anderson model of disordered solids where the anisotropy between the x direction and the y – z plane can be controlled by adjusting an experimentally accessible parameter. This allows us to study experimentally the disorder versus anisotropy phase diagram of the Anderson metal–insulator transition. Numerical and experimental data compare very well with each other and a theoretical analysis based on the self-consistent theory of localization correctly describes the observed behavior, illustrating the flexibility of cold-atom experiments for the study of transport phenomena in complex quantum systems.New Journal of Physics 01/2013; 15(6):065013. · 4.06 Impact Factor

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