3,634 research outputs found
Deformation of dual Leibniz algebra morphisms
An algebraic deformation theory of morphisms of dual Leibniz algebras is
obtained.Comment: 10 pages. To appear in Communications in Algebr
Hom-quantum groups I: quasi-triangular Hom-bialgebras
We introduce a Hom-type generalization of quantum groups, called
quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative
analogues of Drinfel'd's quasi-triangular bialgebras, in which the
non-(co)associativity is controlled by a twisting map. A family of
quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular
bialgebra, such as Drinfel'd's quantum enveloping algebras. Each
quasi-triangular Hom-bialgebra comes with a solution of the quantum
Hom-Yang-Baxter equation, which is a non-associative version of the quantum
Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained
from modules of suitable quasi-triangular Hom-bialgebras.Comment: 21 page
Zooming in on local level statistics by supersymmetric extension of free probability
We consider unitary ensembles of Hermitian NxN matrices H with a confining
potential NV where V is analytic and uniformly convex. From work by
Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit
of the characteristic function for a finite-rank Fourier variable K is
determined by the Voiculescu R-transform, a key object in free probability
theory. Going beyond these results, we argue that the same holds true when the
finite-rank operator K has the form that is required by the Wegner-Efetov
supersymmetry method of integration over commuting and anti-commuting
variables. This insight leads to a potent new technique for the study of local
statistics, e.g., level correlations. We illustrate the new technique by
demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section
Topological Censorship
All three-manifolds are known to occur as Cauchy surfaces of asymptotically
flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove
here the conjecture that general relativity does not allow an observer to probe
the topology of spacetime: any topological structure collapses too quickly to
allow light to traverse it. More precisely, in a globally hyperbolic,
asymptotically flat spacetime satisfying the null energy condition, every
causal curve from \scri^- to {\scri}^+ is homotopic to a topologically
trivial curve from \scri^- to {\scri}^+. (If the Poincar\'e conjecture is
false, the theorem does not prevent one from probing fake 3-spheres).Comment: 12 pages, REVTEX; 1 postscript figure in a separate uuencoded file.
Our earlier version (PRL 71, 1486 (1993)) contained a secondary result,
mistakenly attributed to Schoen and Yau, regarding ``passive topological
censorship'' of a certain class of topologies. As Gregory Burnett has pointed
out (gr-qc/9504012), this secondary result is false. The main topological
censorship theorem is unaffected by the erro
Curvature-dimension inequalities and Li-Yau inequalities in sub-Riemannian spaces
In this paper we present a survey of the joint program with Fabrice Baudoin
originated with the paper \cite{BG1}, and continued with the works \cite{BG2},
\cite{BBG}, \cite{BG3} and \cite{BBGM}, joint with Baudoin, Michel Bonnefont
and Isidro Munive.Comment: arXiv admin note: substantial text overlap with arXiv:1101.359
Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits
We present and discuss the derivation of a nonlinear non-local
integro-differential equation for the macroscopic time evolution of the
conserved order parameter of a binary alloy undergoing phase segregation. Our
model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics,
i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to
the Gibbs measure for a Hamiltonian which includes both short range (local) and
long range (nonlocal) interactions. A rigorous derivation is presented in the
case in which there is no local interaction. In a subsequent paper (part II),
we discuss the phase segregation phenomena in the model. In particular we argue
that the phase boundary evolutions, arising as sharp interface limits of the
family of equations derived in this paper, are the same as the ones obtained
from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page
Evaluating quasilocal energy and solving optimal embedding equation at null infinity
We study the limit of quasilocal energy defined in [7] and [8] for a family
of spacelike 2-surfaces approaching null infinity of an asymptotically flat
spacetime. It is shown that Lorentzian symmetry is recovered and an
energy-momentum 4-vector is obtained. In particular, the result is consistent
with the Bondi-Sachs energy-momentum at a retarded time. The quasilocal mass in
[7] and [8] is defined by minimizing quasilocal energy among admissible
isometric embeddings and observers. The solvability of the Euler-Lagrange
equation for this variational problem is also discussed in both the
asymptotically flat and asymptotically null cases. Assuming analyticity, the
equation can be solved and the solution is locally minimizing in all orders. In
particular, this produces an optimal reference hypersurface in the Minkowski
space for the spatial or null exterior region of an asymptotically flat
spacetime.Comment: 22 page
- …