相关论文: Density-Density Correlators in Infinite Random Mat…

An independent pair ansatz is developed for the many body wavefunction of dilute Bose systems. The pair correlation is optimized by minimizing the expectation value of the full hamiltonian (rather than the truncated Bogoliubov one)…

We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the…

We consider large random matrices $X$ with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical…

We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families…

The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement…

In a previous contribution (H.J. Stoeckmann, J. Phys. A35, 5165 (2002)), the density of states was calculated for a billiard with randomly distributed delta-like scatterers, doubly averaged over the positions of the impurities and the…

We study the average bipartite entanglement entropy of Haar-random pure states in quantum many-body systems with global $\mathrm{SU}(2)$ symmetry, constrained to fixed total spin $J$ and magnetization $J_z = 0$. Focusing on spin-$\tfrac12$…

We consider a two dimensional random band matrix ensemble, in the limit of infinite volume and fixed but large band width $W$. For this model we rigorously prove smoothness of the averaged density of states. We also prove that the resulting…

I revisit the infinite-size variant of the Density Matrix Renormalization Group (iDMRG) algorithm for obtaining a fixed-point translationally invariant matrix product wavefunction in the context of one-dimensional quantum systems. A crucial…

We show that any quantum density matrix can be represented by a Bayesian network (a directed acyclic graph), and also by a Markov network (an undirected graph). We show that any Bayesian or Markov net that represents a density matrix, is…

We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The…

Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic,…

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…

Without any knowledge of the symmetry existing in the system, we derive the exact forms of the order parameters which show long-range correlation in the ground state of the one-dimensional extended Hubbard model using a quantum information…

We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of…

We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing…

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 study a single 2d Dirac fermion at finite density, subject to a quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1d chiral fermions (associated to each point…

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and…

We calculate the `exact' potential corresponding to a one-dimensional interacting system of two electrons with a specific, tailored density. We use one-dimensional density-functional theory with a local-density approximation (LDA) on the…