3,911 research outputs found
Analysis of the divide-and-conquer method for electronic structure calculations
We study the accuracy of the divide-and-conquer method for electronic
structure calculations. The analysis is conducted for a prototypical subdomain
problem in the method. We prove that the pointwise difference between electron
densities of the global system and the subsystem decays exponentially as a
function of the distance away from the boundary of the subsystem, under the gap
assumption of both the global system and the subsystem. We show that gap
assumption is crucial for the accuracy of the divide-and-conquer method by
numerical examples. In particular, we show examples with the loss of accuracy
when the gap assumption of the subsystem is invalid
Quantum transmission in disordered insulators: random matrix theory and transverse localization
We consider quantum interferences of classically allowed or forbidden
electronic trajectories in disordered dielectrics. Without assuming a directed
path approximation, we represent a strongly disordered elastic scatterer by its
transmission matrix . We recall how the eigenvalue distribution of
can be obtained from a certain ansatz leading to a
Coulomb gas analogy at a temperature which depends on the system
symmetries. We recall the consequences of this random matrix theory for
quasi-- insulators and we extend our study to microscopic three dimensional
models in the presence of transverse localization. For cubes of size , we
find two regimes for the spectra of as a function of the
localization length . For , the eigenvalue spacing
distribution remains close to the Wigner surmise (eigenvalue repulsion). The
usual orthogonal--unitary cross--over is observed for {\it large} magnetic
field change where denotes the flux
quantum. This field reduces the conductance fluctuations and the average
log--conductance (increase of ) and induces on a given sample large
magneto--conductance fluctuations of typical magnitude similar to the sample to
sample fluctuations (ergodic behaviour). When is of the order of theComment: Saclay-S93/025 Email: [email protected]
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