18,659 research outputs found
Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory
An overview of several recent developments in density functional theory for
classical inhomogeneous liquids is given. We show how Levy's constrained search
method can be used to derive the variational principle that underlies density
functional theory. An advantage of the method is that the Helmholtz free energy
as a functional of a trial one-body density is given as an explicit expression,
without reference to an external potential as is the case in the standard
Mermin-Evans proof by reductio ad absurdum. We show how to generalize the
approach in order to express the internal energy as a functional of the
one-body density distribution and of the local entropy distribution. Here the
local chemical potential and the bulk temperature play the role of Lagrange
multipliers in the Euler-Lagrange equations for minimiziation of the
functional. As an explicit approximation for the free-energy functional for
hard sphere mixtures, the diagrammatic structure of Rosenfeld's fundamental
measure density unctional is laid out. Recent extensions, based on the
Kierlik-Rosinberg scalar weight functions, to binary and ternary non-additive
hard sphere mixtures are described.Comment: 15 pages, 6 figure
Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons
Both in string field theory and in p-adic string theory the equations of
motion involve infinite number of time derivatives. We argue that the initial
value problem is qualitatively different from that obtained in the limit of
many time derivatives in that the space of initial conditions becomes strongly
constrained. We calculate the energy-momentum tensor and study in detail time
dependent solutions representing tachyons rolling on the p-adic string theory
potentials. For even potentials we find surprising small oscillations at the
tachyon vacuum. These are not conventional physical states but rather
anharmonic oscillations with a nontrivial frequency--amplitude relation. When
the potentials are not even, small oscillatory solutions around the bottom must
grow in amplitude without a bound. Open string field theory resembles this
latter case, the tachyon rolls to the bottom and ever growing oscillations
ensue. We discuss the significance of these results for the issues of emerging
closed strings and tachyon matter.Comment: 46 pages, 14 figures, LaTeX. Replaced version: Minor typos corrected,
some figures edited for clarit
Buildings, spiders, and geometric Satake
Let G be a simple algebraic group. Labelled trivalent graphs called webs can
be used to product invariants in tensor products of minuscule representations.
For each web, we construct a configuration space of points in the affine
Grassmannian. Via the geometric Satake correspondence, we relate these
configuration spaces to the invariant vectors coming from webs. In the case G =
SL(3), non-elliptic webs yield a basis for the invariant spaces. The
non-elliptic condition, which is equivalent to the condition that the dual
diskoid of the web is CAT(0), is explained by the fact that affine buildings
are CAT(0).Comment: 49 pages; revised and to appear in Compositio Mathematic
Subleading Power Factorization in
We analyze the factorization to subleading power in the flavor changing
neutral current process . In particular, we
compute the so-called resolved contributions and explore the numerical impact
on observables. In these contributions the virtual photon couples to light
partons instead of connecting directly to the effective weak-interaction
vertex. They represent an irreducible uncertainty in the inclusive decay which cannot be removed by relaxing the experimentally
necessary cuts in the hadronic mass spectrum.Comment: 32 pages,18 figure
Algebraic constructive quantum field theory: Integrable models and deformation techniques
Several related operator-algebraic constructions for quantum field theory
models on Minkowski spacetime are reviewed. The common theme of these
constructions is that of a Borchers triple, capturing the structure of
observables localized in a Rindler wedge. After reviewing the abstract setting,
we discuss in this framework i) the construction of free field theories from
standard pairs, ii) the inverse scattering construction of integrable QFT
models on two-dimensional Minkowski space, and iii) the warped convolution
deformation of QFT models in arbitrary dimension, inspired from non-commutative
Minkowski space.Comment: Review article, 57 pages, 3 figure
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