Related papers: Multifractality and quantum diffusion from self-co…
Based on the mathematical arguments formulated within the Multifractal Detrended Fluctuation Analysis (MFDFA) approach it is shown that in the uncorrelated time series from the Gaussian basin of attraction the effects resembling…
The paper considers the wave equation, with constant or variable coefficients in $\R^n$, with odd $n\geq 3$. We study the asymptotics of the distribution $\mu_t$ of the random solution at time $t\in\R$ as $t\to\infty$. It is assumed that…
We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W-functional of the…
We consider the phenomenon of weak localization of a short wave pulse in a quasi-1D disordered waveguide. We show that the long-time decay of the average transmission coefficient is not purely exponential, in contradiction with predictions…
In a recent comment, M. Kosterlitz described how the discrepancy about the lack of broken translational symmetry in two dimensions - doubting the existence of 2D crystals - and the first computer simulations foretelling 2D crystals at least…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
We report a systematic and detailed numerical study of statistics of the reflection coefficient $(|R(L)|^2)$ and its associated phase ($\theta$) for a plane wave reflected from a one-dimensional (1D) disordered medium beyond the random…
We develop a model based on a multiple scattering theory to describe the diffusion of polarized light in disordered media exhibiting short-range structural correlations. Starting from exact expressions of the average field and the field…
We show that under quite general conditions, various multifractal spectra may be obtained as Legendre transforms of functions $T\colon \RR\to \RR$ arising in the thermodynamic formalism. We impose minimal requirements on the maps we…
We study numerically multifractal properties of two models of one-dimensional quantum maps, a map with pseudointegrable dynamics and intermediate spectral statistics, and a map with an Anderson-like transition recently implemented with cold…
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of…
We study a system of two coupled kicked rotors, both classically and quantum mechanically, for a wide range of coupling parameters. This was motivated by two published reports, one of which reported quantum localization, while the other…
Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality…
The interplay between electron-electron interactions and weak localization (or anti-localization) phenomena in two-dimensional systems can significantly enhance the superconducting transition temperature. We develop the theory of quantum…
We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the…
Interactions between inertia-gravity waves and balanced flows lead to a spectral diffusion of wave action. Prior work has established that this diffusion is weak across constant frequency surfaces in three-dimensional settings, but can be…
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant…
By calculating all terms of the high-density expansion of the euclidean random matrix theory (up to second-order in the inverse density) for the vibrational spectrum of a topologically disordered system we show that the low-frequency…