Related papers: Disordered statistical physics in low dimensions: …
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…
We revisit the problem of an elastic line (e.g. a vortex line in a superconductor) subject to both columnar disorder and point disorder in dimension $d=1+1$. Upon applying a transverse field, a delocalization transition is expected, beyond…
From the random matrix theory all the energy levels should be strongly correlated due to the presence of all off-diagonal entries.In this work we introduce two new statistics to more accurately characterize these long-distance interactions…
Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models…
We investigate the electric-field driven power-law random banded matrix(PLRBM) model where a variation in the power-law exponent $\alpha$ yields a delocalization-to-localization phase transition. We examine the periodically driven PLRBM…
Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at…
One fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept, challenging our…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
We suggest that if a localized phase at nonzero temperature $T>0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and $T$ is very high.…
System of Dirac fermions with random-varying mass is studied in detail. We reformulate the system by transfer-matrix formalism. Eigenvalues and wave functions are obtained numerically for various configurations of random telegraphic mass…
We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded…
Localized states in one-dimensional open disordered systems and their connection to the internal structure of random samples have been studied. It is shown that the localization of energy and anomalously high transmission associated with…
The equilibrium behavior of a system of elastic layers under tension in the presence of correlated disorder is studied using functional renormalization group techniques. The model exhibits many of the features of the Bose glass phase of…
This work provide a thorough study of L\'evy or heavy-tailed random matrices (LM). By analysing the self-consistent equation on the probability distribution of the diagonal elements of the resolvent we establish the equation determining the…
We consider a two-dimensional electron gas with long range disorder. Assuming that time reversal symmetry is broken either by an external magnetic field or, as in the case of a delta-correlated random magnetic field, by the disorder itself,…
Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…
We introduce and study a new class of Banded Random Matrix model describing sparse, long range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and mappings to statistical physics models, we…
The dynamics of two-dimensional fluids confined within a random matrix of obstacles is investigated using both colloidal model experiments and molecular dynamics simulations. By varying fluid and matrix area fractions in the experiment, we…
We study localization properties of disordered bosons and spins in random fields at zero temperature. We focus on two representatives of different symmetry classes, hard-core bosons (XY magnets) and Ising magnets in random transverse…
We address systematically an apparent non-physical behavior of the free energy moment generating function for several instances of the logarithmically correlated models: the Fractional Brownian Motion with Hurst index $H = 0$ (fBm0) (and…