Related papers: Statistics and Scaling in Disordered Mesoscopic El…
We analyze the role of spectral diffusion in the problem of many-body delocalization in quantum dots and in extended systems. The spectral diffusion parametrically enhances delocalization, modifying the scaling of the delocalization…
The quantum to classical transition has been shown to depend on a number of parameters. Key among these are a scale length for the action, $\hbar$, a measure of the coupling between a system and its environment, $D$, and, for chaotic…
One way to look for complex behaviours in many-body quantum systems is to let the number $N$ of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as $1/N$ tend to commute, whence complexity…
We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and…
In delocalized systems, particle number fluctuations, also known as quantum surface roughness, and the mean-square displacement exhibit a temporal power-law growth followed by a saturation to a system-size-dependent value. We use simple…
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling…
Based on the order parameter expansion, we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations: one for the global, mean field, variable and two…
We report on the comprehensive numerical study of the fluctuation and correlation properties of wave functions in three-dimensional mesoscopic diffusive conductors. Several large sets of nanoscale samples with finite metallic conductance,…
We investigate the finite-size scaling behavior of the conductivity in a two-dimensional Dirac electron gas within a chiral sigma model. Based on the fact that the conductivity is a function of system size times scattering rate, we obtain a…
We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of…
The standard one-parameter scaling theory predicts that all eigenstates in two-dimensional random lattices are weakly localized. We show that this claim fails in two-dimensional dipolar Frenkel exciton systems. The linear energy dispersion…
Quantum coherence and phase transitions are studied in a finite one-dimensional Bose--Hubbard model using exact diagonalization under thermal fluctuations, a Stark potential, and disorder. The condensate fraction, superfluid fraction,…
The aim of this review is to show how ``ferromagnetic'' states, that is, states having a fully polarization, can produce intrinsic decoherence by unitary evolution. This effect can give an understanding of recent experiments on mesoscopic…
The localization properties of electrons moving in a plane perpendicular to a spatially-correlated static magnetic field of random amplitude and vanishing mean are investigated. We apply the method of level statistics to the eigenvalues and…
Recently we have shown that a one-parameter scaling, $T_{coh}$, describes the physical behavior of several heavy fermions in a region of their phase diagram. In this paper we fully characterize this region, obtaining the uniform…
These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…
Mesoscopic conductors are electronic systems of sizes in between nano- and micrometers, and often of reduced dimensionality. In the phase-coherent regime at low temperatures, the conductance of these devices is governed by quantum…
We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the…
Using a quantum map version of one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with quantum standard map. Existence of…
One dimensional systems are under intense investigation, both from theoretical and experimental points of view, since they have rather peculiar characteristics which are of both conceptual and technological interest. We analyze the…