Related papers: Eigenvalue statistics of reduced density matrix du…
Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of modulus 1. We consider the corresponding eigenfunctions, and in Theorem 1.1 we prove that the limit inferior of the ergodic…
We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…
This is a short review of the statistical mechanical definition of entropy production for systems composed of a large number of interacting components. Emphasis is on open systems driven away from equilibrium where the entropy production…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
We study joint eigenvector distributions for large symmetric matrices in the presence of weak noise. Our main result asserts that every submatrix in the orthogonal matrix of eigenvectors converges to a multidimensional Gaussian…
We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the…
The single-parameter scaling hypothesis relating the average and variance of the logarithm of the conductance is a pillar of the theory of electronic transport. We use a maximum-entropy ansatz to explore the logarithm of the energy density,…
We present a new framework for computing low frequency transport properties of strongly correlated, ergodic systems. Our main assumption is that, when a thermalizing diffusive system is driven at frequency $\omega$, domains of size $\xi…
The connection between the non-equilibrium dynamics of isolated quantum many-body systems and statistical mechanics is a fundamental open question. It is generally believed that the unitary quantum evolution of a sufficiently complex system…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…
We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these…
The dynamics of atomic hydrogen placed in a static electric field and illuminated by elliptically polarized microwaves is studied in the range of small field amplitudes where perturbation calculations are applicable. For a general…
An isolated quantum system is said to thermalize if ${\rm Tr} (A \rho(t)) \to {\rm Tr} (A \rho_{\rm eq})$ for time $t \to \infty$. Here $\rho(t)$ is the time-dependent density matrix of the system, $\rho_{\rm eq}$ is the time-independent…
Motivated to understand the asymptotic behavior of periodically driven thermodynamic systems, we study the prototypical example of Brownian particle, overdamped and underdamped, in harmonic potentials subjected to periodic driving. The…
The Wigner-Gaudin-Mehta-Dyson conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of the matrix ensemble. For invariant matrix models, the…
Sample space reducing (SSR) processes offer a simple analytical way to understand of the origin and ubiquity of power-laws in many path-dependent complex systems. SRR processes show a wide range of applications that range from fragmentation…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective…
We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of…
Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining…