Related papers: Sub-diffusion in the Anderson model on random regu…
Disorder can fundamentally modify the transport properties of a system. A striking example is Anderson localization, suppressing transport due to destructive interference of propagation paths. In inhomogeneous many-body systems, not all…
Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{\delta^2}$ of individual particles remains a random variable while indicating that the particle…
We report a new result concerning the dynamics of an initially localized wave packet in quantum nonlinear Schr\"odinger lattices with a disordered potential. A class of nonlinear lattices with subquadratic power nonlinearity is considered.…
We find that Anderson localization ceases to exist when a random medium begins to move, but another type of fundamental quantum effect, Planckian diffusion $D = \alpha\hbar/m$, rises to replace it, with $\alpha $ of order of unity.…
Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an…
We study the relaxation of a diffusive particle confined in an arbitrary external potential and subject to a non-Markovian resetting protocol. With a constant rate $r$, a previous time $\tau$ between the initial time and the present time…
We investigate dynamical scaling properties of the 1D tight-binding Anderson model with a weak diagonal disorder, by means of the spreading of a wave packet. In the absence of disorder, and more generally in the ballistic regime, the…
We study the multi-particle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multi-particle lower edges of…
We address the interplay between two fundamentally different wavepacket localization mechanisms, namely resonant dynamic localization due to collapse of quasi-energy bands in periodic media and disorder-induced Anderson localization.…
We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a…
Diffusion of electrons in a two-dimensional system in static random magnetic fields is studied by solving the time-dependent Schr\"{o}dinger equation numerically. The asymptotic behaviors of the second moment of the wave packets and the…
We report a first-principles study of static transport of localized waves in quasi-one-dimensional open media. We found that such transport, dominated by disorder-induced resonant transmissions, displays novel diffusive behavior. Our…
We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schr\"odinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization…
We study transport in a one-dimensional boundary-driven Anderson insulator (the XX spin chain with onsite disorder) with randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a…
The position $x(t)$ of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray $x=v_0 t$, where $v_0$ is the average drift. However,…
We investigate the motion of a single particle moving on a two-dimensional square lattice whose sites are occupied by right and left rotators. These left and right rotators deterministically rotate the particle's velocity to the right or…
We extend to the two-particle Anderson model the characterization of the metal-insulator transport transition obtained in the one-particle setting by Germinet and Klein. We show that, for any fixed number of particles, the slow spreading of…
Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random…
Anderson localization confines the wave function of a quantum particle in a one-dimensional random potential to a volume of the order of the localization length $\xi$. Nonlinear add-ons to the wave dynamics mimic many-body interactions on a…
The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in…