Related papers: Random Matrix Statistics in Propagating Correlatio…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
Propagation in quantum walks is revisited by showing that very general 1D discrete-time quantum walks with time- and space-dependent coefficients can be described, at the continuous limit, by Dirac fermions coupled to electromagnetic…
We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…
A classification of dynamical systems in terms of their variational properties is reviewed. Within this classification, front propagation is discussed in a non-gradient relaxational potential flow. The model is motivated by transient…
We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow…
We consider the asymptotic behaviour of a family of unidimensional lattice fermion models, which are in exact correspondence with certain probability laws on partitions and on unitary matrices. These models exhibit limit shapes, and in the…
We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe…
We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…
A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on…
We study fluctuation properties of embedded random matrix ensembles of non-interacting particles. For ensemble of two non-interacting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are…
Entanglement fluctuations associated with Schr\"{o}dinger evolution of wavefunctions offer a unique perspective on various fundamental issues ranging from quantum thermalization to state preparation in quantum devices. Very recently, a…
We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the…
We extend the semiclassical picture for the spreading of entanglement and correlations to quantum quenches with several species of quasiparticles that have non-trivial pair correlations in momentum space. These pair correlations are, for…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
We consider non-Hermitian dynamics of a quantum particle hopping on a one-dimensional tight-binding lattice made of $N$ sites with asymmetric hopping rates induced by a time-periodic oscillating imaginary gauge field. A deeply different…
Having established the fact that interacting classical kicked rotor systems exhibit long-lived prethermal phase with quasi-conserved average Hamiltonian before entering into chaotic heating regime, we use spatio-temporal fluctuation…
We study a model of free fermions on a chain with dynamics generated by random unitary gates acting on nearest neighbor bonds and present an exact calculation of time-ordered and out-of-time-ordered correlators. We consider three distinct…
We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any…