Related papers: Random Matrix Statistics in Propagating Correlatio…
We analyze eigenvalues fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that nearest neighbor spacing distribution of…
We study the sudden expansion of strongly correlated fermions in a one-dimensional lattice, utilizing the time-dependent density-matrix renormalization group method. Our focus is on the behavior of experimental observables such as the…
We study the spatio-temporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. We consider systems initially in an uncorrelated state, and find that correlations…
In this paper, we view fluctuating fronts made of particles on a one-dimensional lattice as an extreme value problem. The idea is to denote the configuration for a single front realization at time $t$ by the set of co-ordinates…
Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School "Stochastic…
For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the general parameter dependent distribution between two sets of eigenvalues with two different parameter values can be expressed as a quaternion…
In the first part of the article, we study one-dimensional noninteracting fermions in the continuum and in the presence of the repulsive inverse power law potential, with an emphasis on the Wigner function in the semiclassical limit. In…
We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the…
The statistics of S-matrix fluctuations are numerically investigated on a model for irregular quantum scattering in which a classical chaotic diffusion takes place within the interaction region. Agreement with various random-matrix…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
We study the variational solution of generic interacting fermionic lattice systems using fermionic Gaussian states and show that the process of "gaussification", leading to a nonlinear closed equation of motion for the covariance matrix, is…
We derive a dynamical bound on the propagation of correlations in local random quantum circuits - lattice spin systems where piecewise quantum operations - in space and time - occur with classical probabilities. Correlations are quantified…
Consider an $n \times n$ non-Hermitian random matrix $M_n$ whose entries are independent real random variables. Under suitable conditions on the entries, we study the fluctuations of the entries of $f(M_n)$ as $n$ tends to infinity, where…
Propagation of transition fronts in models of coupled oscillators with non-degenerate on-site potential is usually considered in terms of travelling waves. We show that the system dynamics can be reformulated as an implicit map structure,…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…
Relaxation in the time correlation between operators is studied. Quantized chaotic systems are shown to have distinct relaxation fluctuations that are universal and can be usefully modelled by Random Matrix Theory. Various quantized maps…
We consider the quantum centipede made of $N$ fermionic quantum walkers on the one-dimensional lattice interacting by means of the simplest of all hard-bound constraints: the distance between two consecutive fermions is either one or two…
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
We revisit the out-of-equilibrium physics arising during the unitary evolution of a one-dimensional XXZ spin chain initially prepared in a domain wall state $\vert\psi_0\rangle=\vert\dots \uparrow\uparrow\downarrow\downarrow\dots\rangle$.…
I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof, featuring low-energy two- and…