335,384 research outputs found
Chemical Hardness, Linear Response, and Pseudopotential Transferability
We propose a systematic method of analyzing pseudopotential transferability
based on linear-response properties of the free atom, including self-consistent
chemical hardness and polarizability. Our calculation of hardness extends the
approach of Teter\cite{teter} not only by including self-consistency, but also
by generalizing to non-diagonal hardness matrices, thereby allowing us to test
for transferability to non-spherically symmetric environments. We apply the
method to study the transferability of norm-conserving pseudopotentials for a
variety of elements in the Periodic Table. We find that the self-consistent
corrections are frequently significant, and should not be neglected. We prove
that the partial-core correction improves the pseudopotential hardness of
alkali metals considerably. We propose a quantity to represent the average
hardness error and calculate this quantity for many representative elements as
a function of pseudopotential cutoff radii. We find that the atomic
polarizabilities are usually well reproduced by the norm-conserving
pseudopotentials. Our results provide useful guidelines for making optimal
choices in the pseudopotential generation procedure.Comment: Revtex (preprint style, 33 pages) + 9 postscript figures A version in
two-column article style with embedded figures is available at
http://electron.rutgers.edu/~dhv/preprints/index.html#l
The random geometry of equilibrium phases
This is a (long) survey about applications of percolation theory in
equilibrium statistical mechanics. The chapters are as follows:
1. Introduction
2. Equilibrium phases
3. Some models
4. Coupling and stochastic domination
5. Percolation
6. Random-cluster representations
7. Uniqueness and exponential mixing from non-percolation
8. Phase transition and percolation
9. Random interactions
10. Continuum modelsComment: 118 pages. Addresses: [email protected]
http://www.mathematik.uni-muenchen.de/~georgii.html [email protected]
http://www.math.chalmers.se/~olleh [email protected]
Quantum Equilibrium and the Origin of Absolute Uncertainty
The quantum formalism is a ``measurement'' formalism--a phenomenological
formalism describing certain macroscopic regularities. We argue that it can be
regarded, and best be understood, as arising from Bohmian mechanics, which is
what emerges from Schr\"odinger's equation for a system of particles when we
merely insist that ``particles'' means particles. While distinctly
non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles
in motion, a motion choreographed by the wave function. We find that a Bohmian
universe, though deterministic, evolves in such a manner that an {\it
appearance} of randomness emerges, precisely as described by the quantum
formalism and given, for example, by ``\rho=|\psis|^2.'' A crucial ingredient
in our analysis of the origin of this randomness is the notion of the effective
wave function of a subsystem, a notion of interest in its own right and of
relevance to any discussion of quantum theory. When the quantum formalism is
regarded as arising in this way, the paradoxes and perplexities so often
associated with (nonrelativistic) quantum theory simply evaporate.Comment: 75 pages. This paper was published a long time ago, but was never
archived. We do so now because it is basic for our recent article
quant-ph/0308038, which can in fact be regarded as an appendix of the earlier
on
Metastable States in Spin Glasses and Disordered Ferromagnets
We study analytically M-spin-flip stable states in disordered short-ranged
Ising models (spin glasses and ferromagnets) in all dimensions and for all M.
Our approach is primarily dynamical and is based on the convergence of a
zero-temperature dynamical process with flips of lattice animals up to size M
and starting from a deep quench, to a metastable limit. The results (rigorous
and nonrigorous, in infinite and finite volumes) concern many aspects of
metastable states: their numbers, basins of attraction, energy densities,
overlaps, remanent magnetizations and relations to thermodynamic states. For
example, we show that their overlap distribution is a delta-function at zero.
We also define a dynamics for M=infinity, which provides a potential tool for
investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review
Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications
We use the halo model of clustering to compute two- and three-point
correlation functions for weak lensing, and apply them in a new statistical
technique to measure properties of massive halos. We present analytical results
on the eight shear three-point correlation functions constructed using
combination of the two shear components at each vertex of a triangle. We
compare the amplitude and configuration dependence of the functions with
ray-tracing simulations and find excellent agreement for different scales and
models. These results are promising, since shear statistics are easier to
measure than the convergence. In addition, the symmetry properties of the shear
three-point functions provide a new and precise way of disentangling the
lensing E-mode from the B-mode due to possible systematic errors.
We develop an approach based on correlation functions to measure the
properties of galaxy-group and cluster halos from lensing surveys. Shear
correlations on small scales arise from the lensing matter within halos of mass
M > 10^13 solar masses. Thus the measurement of two- and three-point
correlations can be used to extract information on halo density profiles,
primarily the inner slope and halo concentration. We demonstrate the
feasibility of such an analysis for forthcoming surveys. We include covariances
in the correlation functions due to sample variance and intrinsic ellipticity
noise to show that 10% accuracy on profile parameters is achievable with
surveys like the CFHT Legacy survey, and significantly better with future
surveys. Our statistical approach is complementary to the standard approach of
identifying individual objects in survey data and measuring their properties.Comment: 30 pages, 21 figures. Corrected typos in equations (23) and (28).
Matches version for publication in MNRA
Spontaneous symmetry breaking: exact results for a biased random walk model of an exclusion process
It has been recently suggested that a totally asymmetric exclusion process
with two species on an open chain could exhibit spontaneous symmetry breaking
in some range of the parameters defining its dynamics. The symmetry breaking is
manifested by the existence of a phase in which the densities of the two
species are not equal. In order to provide a more rigorous basis to these
observations we consider the limit of the process when the rate at which
particles leave the system goes to zero. In this limit the process reduces to a
biased random walk in the positive quarter plane, with specific boundary
conditions. The stationary probability measure of the position of the walker in
the plane is shown to be concentrated around two symmetrically located points,
one on each axis, corresponding to the fact that the system is typically in one
of the two states of broken symmetry in the exclusion process. We compute the
average time for the walker to traverse the quarter plane from one axis to the
other, which corresponds to the average time separating two flips between
states of broken symmetry in the exclusion process. This time is shown to
diverge exponentially with the size of the chain.Comment: 42 page
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