Related papers: Statistics of matrix elements of local operators i…
We study scaling properties of the localized eigenstates of the random dimer model in which pairs of local site energies are assigned at random in a one dimensional disordered tight-binding model. We use both the transfer matrix method and…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
Localization to delocalization transitions in eigenfunctions are studied for finite interacting boson systems by employing one- plus two-body embedded Gaussian orthogonal ensemble of random matrices [EGOE(1+2)]. In the first analysis,…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an alternative…
In this paper, a purely measurement-based method is proposed to estimate the dynamic system state matrix by applying the regression theorem of the multivariate Ornstein-Uhlenbeck process. The proposed method employs a recursive algorithm to…
We study the level statistics of a non-integrable one dimensional interacting fermionic system characterized by the GOE distribution. We calculate numerically on a finite size system the level spacing distribution $P(s)$ and the Dyson-Mehta…
The Eigenstate Thermalization Hypothesis explains thermalization in isolated quantum systems through the statistical properties of observables in the energy eigenbasis. We investigate the crossover from integrability to chaos in the…
The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement present in its pure ground state. In this work, we establish scaling laws for this entanglement for critical quasi-free fermionic and…
For quantum lattice systems with local interactions, the Lieb-Robinson bound acts as an alternative for the strict causality of relativistic systems and allows to prove many interesting results, in particular when the energy spectrum…
We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centred on the large scale properties of the locally conserved hydrodynamical observables, and our…
The question of thermalization in quantum many-body systems has long been studied through the properties of matrix elements of operators corresponding to local observables. More recently, the focus has shifted to the dynamics of operators,…
The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
This work examines a discrete elastic energy system with local interactions described by a discrete second-order functional in the symmetric gradient and additional non-local random long-range interactions. We analyze the asymptotic…
Eigenvalue correlations of random matrix ensembles as a function of an external perturbation are investigated vis the Dyson Brownian Motion Model in the situation where the level density has a hard edge singularity. By solving a linearized…
We revisit the question of describing critical spin systems and field theories using matrix product states, and formulate a scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice spacing in the case of…
Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across the many-body localization transition (MBLT) in a…
We study a model of interacting fermions in one dimension subject to random, uncorrelated onsite disorder. The model realizes an interaction-driven quantum phase transition between an ergodic and a many-body localized phase (MBL). We…
The quantum cat map is a model for a quantum system with underlying chaotic dynamics. In this paper we study the matrix elements of smooth observables in this model, when taking arithmetic symmetries into account. We give explicit formulas…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…