相关论文: Low density expansion for Lyapunov exponents

The low-energy quasiparticle states of a disordered d-wave superconductor are investigated theoretically. A class of such states, formed via tunneling between the Andreev bound states that are localized around extended impurities (and…

Anderson localization of matter waves was recently observed with cold atoms in a weak 1D disorder realized with laser speckle potential [J. Billy et al., Nature 453, 891 (2008)]. The latter is special in that it does not have spatial…

The phase space trajectories of many body systems charateristic of simple fluids are highly unstable. We quantify this instability by a set of Lyapunov exponents, which are the rates of exponential divergence, or convergence, of initial…

Anomalies are known to appear in the perturbation theory for the one-dimensional Anderson model. A systematic approach to anomalies at critical points of products of random matrices is developed, classifying and analysing their possible…

A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy dependent doubly stochastic matrix, the size of which is proportional to the strip width. This…

We study the density of states in disordered s-wave superconductors with a small gap anisotropy. Disorder comes in the form of common nonmagnetic scatterers and pairing-potential impurities, which interact with electrons via an electric…

Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in…

We use vortex matter in type-II superconductors as a playground to study how different types of disorder affect the long wavelength density fluctuations of the system. We find that irrespective of the vortex-vortex interaction, in the case…

The absence of localization of impurity-induced low-energy quasiparticle states in a two-dimensional $d$-wave superconductor is argued for any amount of disorder in the limit of unitary scatterers. This surprising result follows from the…

The Lyapunov spectrum describes the exponential growth, or decay, of infinitesimal phase-space perturbations. The perturbation associated with the maximum Lyapunov exponent is strongly localized in space, and only a small fraction of all…

The cubic anisotropy model provides a simple example of a system with an arbitrarily weak first-order phase transition. We present an analysis of this model using $\eps$-expansion techniques with results up to next-to-next-to-leading order…

We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are…

We consider 1-D quasi-periodic Frenkel-Kontorova models. We study the existence of equilibria whose frequency (i.e. the inverse of the density of deposited material) is resonant with the frequencies of the substratum. We study perturbation…

Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…

Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance…

We revisit the problem of one-dimensional Anderson localization, by providing perturbative expression for Lyapunov exponent of Anderson model with next-nearest-neighbor (nnn) hopping. By comparison with exact numerical results, we discuss…

We describe a perturbation expansion for the energy and wave function of a weakly bound particle in a short-range potential in one space dimension.

A global phase diagram of disordered weak and strong topological insulators is established numerically. As expected, the location of the phase boundaries is renormalized by disorder, a feature recognized in the study of the so-called…

In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…

Localization of wave functions in disordered systems can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is an analytic…