5,005 research outputs found
Further Evidence for a Gravitational Fixed Point
A theory of gravity with a generic action functional and minimally coupled to
N matter fields has a nontrivial fixed point in the leading large N
approximation. At this fixed point, the cosmological constant and Newton's
constant are nonzero and UV relevant; the curvature squared terms are
asymptotically free with marginal behaviour; all higher order terms are
irrelevant and can be set to zero by a suitable choice of cutoff function.Comment: LaTEX, 4 pages. Relative to the published paper, a sign has been
corrected in equations (17) and (18
Practically linear analogs of the Born-Infeld and other nonlinear theories
I discuss theories that describe fully nonlinear physics, while being
practically linear (PL), in that they require solving only linear differential
equations. These theories may be interesting in themselves as manageable
nonlinear theories. But, they can also be chosen to emulate genuinely nonlinear
theories of special interest, for which they can serve as approximations. The
idea can be applied to a large class of nonlinear theories, exemplified here
with a PL analogs of scalar theories, and of Born-Infeld (BI) electrodynamics.
The general class of such PL theories of electromagnetism are governed by a
Lagrangian L=-(1/2)F_mnQ^mn+ S(Q_mn), where the electromagnetic field couples
to currents in the standard way, while Qmn is an auxiliary field, derived from
a vector potential that does not couple directly to currents. By picking a
special form of S(Q_mn), we can make such a theory similar in some regards to a
given fully nonlinear theory, governed by the Lagrangian -U(F_mn). A
particularly felicitous choice is to take S as the Legendre transform of U. For
the BI theory, this Legendre transform has the same form as the BI Lagrangian
itself. Various matter-of-principle questions remain to be answered regarding
such theories. As a specific example, I discuss BI electrostatics in more
detail. As an aside, for BI, I derive an exact expression for the
short-distance force between two arbitrary point charges of the same sign, in
any dimension.Comment: 20 pages, Version published in Phys. Rev.
Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo
We present a simple and general formalism to compute efficiently the
derivatives of a multi-determinant Jastrow-Slater wave function, the local
energy, the interatomic forces, and similar quantities needed in quantum Monte
Carlo. Through a straightforward manipulation of matrices evaluated on the
occupied and virtual orbitals, we obtain an efficiency equivalent to
algorithmic differentiation in the computation of the interatomic forces and
the optimization of the orbital paramaters. Furthermore, for a large
multi-determinant expansion, the significant computational gain recently
reported for the calculation of the wave function is here improved and extended
to all local properties in both all-electron and pseudopotential calculations.Comment: 15 pages, 3 figure
Application of Fredholm integral equations inverse theory to the radial basis function approximation problem
This paper reveals and examines the relationship between the solution and stability of Fredholm integral equations and radial basis function approximation or interpolation. The underlying system (kernel) matrices are shown to have a smoothing property which is dependent on the choice of kernel. Instead of using the condition number to describe the ill-conditioning, hence only looking at the largest and smallest singular values of the matrix, techniques from inverse theory, particularly the Picard condition, show that it is understanding the exponential decay of the singular values which is critical for interpreting and mitigating instability. Results on the spectra of certain classes of kernel matrices are reviewed, verifying the exponential decay of the singular values. Numerical results illustrating the application of integral equation inverse theory are also provided and demonstrate that interpolation weights may be regarded as samplings of a weighted solution of an integral equation. This is then relevant for mapping from one set of radial basis function centers to another set. Techniques for the solution of integral equations can be further exploited in future studies to find stable solutions and to reduce the impact of errors in the data
Nonlinear Elasticity of the Sliding Columnar Phase
The sliding columnar phase is a new liquid-crystalline phase of matter
composed of two-dimensional smectic lattices stacked one on top of the other.
This phase is characterized by strong orientational but weak positional
correlations between lattices in neighboring layers and a vanishing shear
modulus for sliding lattices relative to each other. A simplified elasticity
theory of the phase only allows intralayer fluctuations of the columns and has
three important elastic constants: the compression, rotation, and bending
moduli, , , and . The rotationally invariant theory contains
anharmonic terms that lead to long wavelength renormalizations of the elastic
constants similar to the Grinstein-Pelcovits renormalization of the elastic
constants in smectic liquid crystals. We calculate these renormalizations at
the critical dimension and find that , where is a wavenumber. The behavior of
, , and in a model that includes fluctuations perpendicular to the
layers is identical to that of the simple model with rigid layers. We use
dimensional regularization rather than a hard-cutoff renormalization scheme
because ambiguities arise in the one-loop integrals with a finite cutoff.Comment: This file contains 18 pages of double column text in REVTEX format
and 6 postscript figure
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