Related papers: Intermediate spectral statistics in the many--body…
We study the combined effect of quasiperiodic disorder, driven and interaction in the periodically kicked Aubry-Andr\'{e} model. In the non-interacting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a…
This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…
The model of Fermi particles with random two-body interaction is investigated. This model allows to study the origin and accuracy of statistical laws in few-body systems, the role of interaction and chaos in thermalization, Fermi-Dirac…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…
The many-body localization transition is a dynamical quantum phase transition between a localized and an extended phase. We study this transition in the XXZ model with disordered magnetic field and focus on the time evolution following a…
In this paper, we employ a semiperturbative theory to study the statistical structural properties of energy eigenfunctions (EFs) in many-body quantum chaotic systems consisting of a central system coupled to an environment. Under certain…
The possible paralelism existing between phase transitions and fracture in disordered materials, is discussed using the well-known Fiber Bundle Models and a probabilistic approach suited to smooth fluctuations near the critical point. Two…
We discover a novel localization transition that alters the dynamics of coherence in disordered many-body spin systems subject to Markovian dissipation. The transition occurs in the middle spectrum of the Lindbladian super-operator whose…
Understanding how the interaction range and various types of disorder affect the level statistics of many-body quantum systems and lead to the emergence of many-body localization (MBL) is a challenging open frontier. We study the level…
A central concern across the natural sciences is a quantitative understanding of the mechanism governing rare transitions between two metastable states. Recent research has uncovered a fundamental equality between the time-reversal…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
Asymptotic normality of intermediate order statistics taken from univariate iid random variables is well-known. We generalize this result to random vectors in arbitrary dimension, where the order statistics are taken componentwise.
We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function…
Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…
We explore the distribution of paths followed in fluctuation-induced switching between coexisting stable states. We introduce a quantitative characteristic of the path distribution in phase space that does not require a priori knowledge of…
The concept of exchange braid statistics is generalized. The cross statistics is studied as a result of interaction. An algebraic model of a system of particles equipped with such statistics is described. The corresponding Fock space…
We study the effects of random fluctuations on quantum phase transitions by the energy gap analysis. For the infinite-ranged spin-glass models with a transverse field, we find that a strong sample-to-sample fluctuation effect leads to broad…
Recent theoretical and numerical evidence suggests that localization can survive in disordered many-body systems with very high energy density, provided that interactions are sufficiently weak. Stronger interactions can destroy…
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…
Gibbs and Boltzmann definitions of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite sized `small' system exchanging energy with a bath is usually understood as a…