Related papers: Thermalization Universality-Class Transition Induc…
The universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality, is…
A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few $M$ frequencies a normal diffusion is realized, but the transition to…
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 explore the interplay of disorder and topological phenomena in honeycomb lattices of atoms coupled by the electromagnetic field. On the one hand, disorder can trigger transitions between distinct topological phases and drive the lattice…
We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of…
Influence of disorder-induced Anderson localization and of electron-electron interaction on superconductivity in two-dimensional systems is explored. We determine the superconducting transition temperature $T_c$, the temperature dependence…
For short-ranged disordered quantum models in one dimension, the Many-Body-Localization is analyzed via the adaptation to the Many-Body context [M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless point of view on the…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
The celebrated Kitaev chain reveals a captivating phase diagram in the presence of various disorders, encompassing multifractal states and topological Anderson phases. In this work, we investigate the localization and topological properties…
The exact probability distributions of the resistance, the conductance and the transmission are calculated for the one-dimensional Anderson model with long-range correlated off-diagonal disorder at E=0. It is proved that despite of the…
We study Anderson localization in a one-dimensional disordered system with long-range correlated hopping decaying as $1/r^{a}$ with complex hopping amplitudes that break time-reversal symmetry in a tunable fashion by varying their argument.…
We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical…
Disorder-induced Anderson localization in quasiparticle transport is a challenging problem to address, even more so in the presence of dissipation as the symptoms of disorder-induced localization are very closely simulated by the absorption…
A generalization of the single-parameter scaling theory of localization is proposed for the case when the random potential depends on temperature. The scaling equation describing the behavior of the resistance is derived. It is shown that…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
A field theory of the Anderson transition in two dimensional disordered systems with spin-orbit interactions and time-reversal symmetry is developed, in which the proliferation of vortex-like topological defects is essential for…
We study the disorder effects upon superconducting transition temperature T_c and the number of local pairs in attractive Hubbard model within the combined Nozieres - Schmitt-Rink and DMFT+\Sigma approximations. We analyze the wide range of…
Anderson localization transitions are usually referred to as quantum phase transitions from delocalized states to localized states in disordered systems. Here we report an unconventional ``Anderson localization transition'' in…
Spectral statistics of disordered systems encode Thouless and Heisenberg time scales whose ratio determines whether the system is chaotic or localized. Identifying similarities between system size and disorder strength scaling of Thouless…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…