Related papers: Prominent interference peaks in the dephasing Ande…
Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here we argue that a scaled…
We present two complementary simulations that lead to an exploration of Anderson localization, a phenomenon in which wave diffusion is suppressed in disordered media by interference from multiple scattering. To build intuition, the first…
We investigate the wave-packet dynamics of the power-law bond disordered one-dimensional Anderson model with hopping amplitudes decreasing as $H_{nm}\propto |n-m|^{-\alpha}$. We consider the critical case ($\alpha=1$). Using an exact…
We numerically model the evolution of a pair of coherently split quasicondensates. A truly one-dimensional case is assumed, so that the loss of the (initially high) coherence between the two quasicondensates is due to dephasing only, but…
Excitonic transport in static disordered one dimensional systems is studied in the presence of thermal fluctuations that are described by the Haken-Strobl-Reineker model. For short times, non-diffusive behavior is observed that can be…
Topological Anderson transitions, which are direct phase transitions between topologically distinct Anderson localised phases, allow for criticality in 1D disordered systems. We analyse the statistical properties of an emsemble of critical…
The present paper provides an overview of results obtained in four recent papers by the authors. These papers address the problem of intermittency for the Parabolic Anderson Model in a \emph{time-dependent random medium}, describing the…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
We study overlap of two different eigenfunctions as compared with self-overlap in the framework of an infinite-dimensional version of the disordered tight-binding model. Despite a very sparse structure of the eigenstates in the vicinity of…
We investigate the emergent open dynamics of a quantum system that undergoes rapid repeated unitary interactions with a sequence of ancillary systems. We study in detail how decoherence appears as a subleading effect when a quantum system…
We consider a ring of identical or near identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the…
A short quasi-monochromatic wave packet incident on a semi-infinite disordered medium gives rise to a reflected wave. The intensity of the latter decays as a power law $1/t^{\alpha}$ in the long-time limit. Using the one-dimensional…
We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both…
An outstanding topic on noise phenomena is the occurrence of peaked structures in many natural systems in a wide range 10^-1 - 10^6 Hz. All existing theories failed to explain this issue. The present theory based on first prin-ciple…
We study the dependence on the spatial dimensionality of different quantities relevant in the description of the Anderson transition by combining numerical calculations in a $3 \leq d \leq 6$ disordered tight binding model with theoretical…
The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…
Anderson localization, i.e. the suppression of diffusion in lattices with random or incommensurate disorder, is a fragile interference phenomenon which is spoiled out in the presence of dephasing effects or fluctuating disorder. As a…
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrodinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior,…
We investigate opinion formation in a kinetic exchange opinion model, where opinions are represented by numbers in the real interval $[-1,1]$ and agents are typified by the individual degree of conviction about the opinion that they…
We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. The coupling to the central site partially dilutes the Anderson localized peak towards the nearly resonant sites.…