Related papers: Approximation of the integrated density of states …
We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…
The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error…
We derive bounds on the integrated density of states for a class of Schr\"odinger operators with a random potential. The potential depends on a sequence of random variables, not necessarily in a linear way. An example of such a random…
We address the problem posed by the inhomogeneous trapping fields when using ultracold fermions to simulate strongly correlated electrons. As a starting point, we calculate the density of states for a single atom. Using semiclassical…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…
We study spectral properties of ergodic random Schr\"odinger operators on $L^2 (\RR^d)$. The density of states is shown to exist for a certain class of alloy type potentials with single site potentials of changing sign. The Wegner estimate…
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…
We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class…
This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…
We derive novel concentration inequalities for the operator norm of the sum of self-adjoint operators that do not explicitly depend on the underlying dimension of the operator, but rather an intrinsic notion of it. Our analysis leads to…
We study multi-particle interactive quantum disordered systems on a polynomially-growing countable connected graph (Z,E). The novelty is to give localization bounds uniform in finite or infinite volumes (subgraphs) in Z^N as well as for the…
Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The algorithm can achieve arbitrarily high-orders of convergence in terms of a…
Using the finite-size effects the scaling dimensions and correlation functions of the main operators in continuous and lattice models of 1d spinless Bose-gas with pairwise interaction of rather general form are obtained. The long-wave…
This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are…
We derive a formula for the entanglement entropy of squeezed states on a lattice in terms of the complex structure J. The analysis involves the identification of squeezed states with group-theoretical coherent states of the symplectic group…
We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing models in approximating higher-order smooth functions,…
A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals.…
We calculate the exact density of states (DOS) for the three classical and two non-classical Random Matrix Ensembles for finite matrix size N using supersymmetric integrals. The 1/N-Expansion yields already in lowest order good…
We investigate spectral properties of a discrete random displacement model, a Schr\"odinger operator on $\ell^2(\Z^d)$ with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of…