7,453 research outputs found
The Decay Properties of the Finite Temperature Density Matrix in Metals
Using ordinary Fourier analysis, the asymptotic decay behavior of the density
matrix F(r,r') is derived for the case of a metal at a finite electronic
temperature. An oscillatory behavior which is damped exponentially with
increasing distance between r and r' is found. The decay rate is not only
determined by the electronic temperature, but also by the Fermi energy. The
theoretical predictions are confirmed by numerical simulations
Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models
Estimating a covariance matrix efficiently and discovering its structure are important statistical problems with applications in many fields. This article takes a Bayesian approach to estimate the covariance matrix of Gaussian data. We use ideas from Gaussian graphical models and model selection to construct a prior for the covariance matrix that is a mixture over all decomposable graphs, where a graph means the configuration of nonzero offdiagonal elements in the inverse of the covariance matrix. Our prior for the covariance matrix is such that the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We give empirical results that show the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the correct decomposable graph and in more efficiently estimating the covariance matrix. The advantage is greatest when the number of observations is small relative to the dimension of the covariance matrix. The article also shows empirically that there is minimal change in statistical efficiency in using the mixture over decomposable graphs prior for estimating a general covariance compared to the Bayesian estimator by Wong et al. (2003), even when the graph of the covariance matrix is nondecomposable. However, our approach has some important advantages over that of Wong et al. (2003). Our method requires the number of decomposable graphs for each graph size. We show how to estimate these numbers using simulation and that the simulation results agree with analytic results when such results are known. We also show how to estimate the posterior distribution of the covariance matrix using Markov chain Monte Carlo with the elements of the covariance matrix integrated out and give empirical results that show the sampler is computationally efficient and converges rapidly. Finally, we note that both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.Covariance selection; Graphical models; Reduced conditional sampling; Variable selection
Lower bounds for the conductivities of correlated quantum systems
We show how one can obtain a lower bound for the electrical, spin or heat
conductivity of correlated quantum systems described by Hamiltonians of the
form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by
conservation laws which lead to an infinite conductivity for g=0. The small
perturbation g H1, however, renders the conductivity finite at finite
temperatures. For example, H0 could be a continuum field theory, where momentum
is conserved, or an integrable one-dimensional model while H1 might describe
the effects of weak disorder. In the limit g to 0, we derive lower bounds for
the relevant conductivities and show how they can be improved systematically
using the memory matrix formalism. Furthermore, we discuss various applications
and investigate under what conditions our lower bound may become exact.Comment: Title changed; 9 pages, 2 figure
Ground-state energy and Wigner crystallization in thick 2D-electron systems
The ground state energy of the 2-D Wigner crystal is determined as a function
of the thickness of the electron layer and the crystal structure. The method of
evaluating the exchange-correlation energy is tested using known results for
the infinitely-thin 2D system. Two methods, one based on the local-density
approximation(LDA), and another based on the constant-density approximation
(CDA) are established by comparing with quantum Monte-Carlo (QMC) results. The
LDA and CDA estimates for the Wigner transition of the perfect 2D fluid are at
and 32 respectively, compared with from QMC. For thick-2D
layers as found in Hetero-junction-insulated-gate field-effect transistors, the
LDA and CDA predictions of the Wigner transition are at and 15.5
respectively. Impurity effects are not considered here.Comment: Last figure and Table are modified in the revised version.
Conclusions regarding the Wigner transition in thick layers are modified in
the revised version. Latex manuscript, four figure
Quasiparticle Electronic structure of Copper in the GW approximation
We show that the results of photoemission and inverse photoemission
experiments on bulk copper can be quantitatively described within
band-structure theory, with no evidence of effects beyond the
single-quasiparticle approximation. The well known discrepancies between the
experimental bandstructure and the Kohn-Sham eigenvalues of Density Functional
Theory are almost completely corrected by self-energy effects.
Exchange-correlation contributions to the self-energy arising from 3s and 3p
core levels are shown to be crucial.Comment: 4 pages, 2 figures embedded in the text. 3 footnotes modified and 1
reference added. Small modifications also in the text. Accepted for
publication in PR
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