4,134 research outputs found
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
Positivity of Quasilocal Mass
Motivated by the important work of Brown adn York on quasilocal energy, we
propose definitions of quasilocal energy and momentum surface energy of a
spacelike 2-surface with positive intrinsic curvature in a spacetime. We show
that the quasilocal energy of the boundary of a compact spacelike hypersurface
which satisfies the local energy condition is strictly positive unless the
spacetime is flat along the spacelike hypersurface.Comment: 4 pages; final published versio
Rigorous Derivation of the Gross-Pitaevskii Equation
The time dependent Gross-Pitaevskii equation describes the dynamics of
initially trapped Bose-Einstein condensates. We present a rigorous proof of
this fact starting from a many-body bosonic Schroedinger equation with a short
scale repulsive interaction in the dilute limit. Our proof shows the
persistence of an explicit short scale correlation structure in the condensate.Comment: 4 pages, 1 figur
The geometry of manifolds and the perception of space
This essay discusses the development of key geometric ideas in the 19th
century which led to the formulation of the concept of an abstract manifold
(which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl
in 1913. This notion of manifold and the geometric ideas which could be
formulated and utilized in such a setting (measuring a distance between points,
curvature and other geometric concepts) was an essential ingredient in
Einstein's gravitational theory of space-time from 1916 and has played
important roles in numerous other theories of nature ever since.Comment: arXiv admin note: substantial text overlap with arXiv:1301.064
Topological String Partition Functions as Polynomials
We investigate the structure of the higher genus topological string
amplitudes on the quintic hypersurface. It is shown that the partition
functions of the higher genus than one can be expressed as polynomials of five
generators. We also compute the explicit polynomial forms of the partition
functions for genus 2, 3, and 4. Moreover, some coefficients are written down
for all genus.Comment: 22 pages, 6 figures. v2:typos correcte
Quantum tunneling on graphs
We explore the tunneling behavior of a quantum particle on a finite graph, in
the presence of an asymptotically large potential. Surprisingly the behavior is
governed by the local symmetry of the graph around the wells.Comment: 18 page
Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II
Consider axisymmetric strong solutions of the incompressible Navier-Stokes
equations in with non-trivial swirl. Let denote the axis of symmetry
and measure the distance to the z-axis. Suppose the solution satisfies
either or, for some \e > 0, for and
allowed to be large. We prove that is regular at time zero.Comment: More explanations and a new appendi
Spintronic single qubit gate based on a quantum ring with spin-orbit interaction
In a quantum ring connected with two external leads the spin properties of an
incoming electron are modified by the spin-orbit interaction resulting in a
transformation of the qubit state carried by the spin. The ring acts as a one
qubit spintronic quantum gate whose properties can be varied by tuning the
Rashba parameter of the spin-orbit interaction, by changing the relative
position of the junctions, as well as by the size of the ring. We show that a
large class of unitary transformations can be attained with already one ring --
or a few rings in series -- including the important cases of the Z, X, and
Hadamard gates. By choosing appropriate parameters the spin transformations can
be made unitary, which corresponds to lossless gates.Comment: 4 pages, 4 figure
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