24,518 research outputs found
On Three Generalizations of Contraction
We introduce three forms of generalized contraction (GC). Roughly speaking,
these are motivated by allowing contraction to take place after small
transients in time and/or amplitude. Indeed, contraction is usually used to
prove asymptotic properties, like convergence to an attractor or entrainment to
a periodic excitation, and allowing initial transients does not affect this
asymptotic behavior.
We provide sufficient conditions for GC, and demonstrate their usefulness
using examples of systems that are not contractive, with respect to any norm,
yet are GC
SYK-like Tensor Models on the Lattice
We study large tensor models on the lattice without disorder. We
introduce techniques which can be applied to a wide class of models, and
illustrate it by studying some specific rank-3 tensor models. In particular, we
study Klebanov-Tarnopolsky model on lattice, Gurau-Witten model (by treating it
as a tensor model on four sites) and also a new model which interpolates
between these two models. In each model, we evaluate various four point
functions at large and strong coupling, and discuss their spectrum and long
time behaviors. We find similarities as well as differences from SYK model. We
also generalize our analysis to rank- tensor models where we obtain
analogous results as case for the four point functions which we computed.
For , we are able to compute the next-to-subleading
corrections for a specific four point function.Comment: 46 pages, 29 figures; v2:typos corrected, reference added; v3:minor
revisions, to be published in JHE
The theory and some applications of Pták's method of non-discrete mathematical induction
Bibliography: p. 79-80.The aim of this thesis is three-fold: (1) to develop the theory of small functions; (2) to synthesize Pták's work presented in his papers [10], [11], ..., [16] into a coherent body of knowledge; (3) to elaborate on Pták's work (i) by providing small function generalizations of Banach's Fixed Point Theorem and Edelstein's Extended Contraction Principle; (ii) by connecting the Induction Theorem to Baire's Category Theorem and Cantor's Intersection Theorem. Throughout the exposition the editorial "we" is to be understood in the sense of Halmos [ 18]; "we" means "the author and the reader"
A New Family of Solvable Self-Dual Lie Algebras
A family of solvable self-dual Lie algebras is presented. There exist a few
methods for the construction of non-reductive self-dual Lie algebras: an
orthogonal direct product, a double-extension of an Abelian algebra, and a
Wigner contraction. It is shown that the presented algebras cannot be obtained
by these methods.Comment: LaTeX, 12 page
Unique characterization of the Bel-Robinson tensor
We prove that a completely symmetric and trace-free rank-4 tensor is, up to
sign, a Bel-Robinson type tensor, i.e., the superenergy tensor of a tensor with
the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a
certain quadratic identity. This may be seen as the first Rainich theory result
for rank-4 tensors.Comment: extended version, 13 pages, shorter version published in
Class.Quant.Gra
Topological Graph Polynomials in Colored Group Field Theory
In this paper we analyze the open Feynman graphs of the Colored Group Field
Theory introduced in [arXiv:0907.2582]. We define the boundary graph
\cG_{\partial} of an open graph \cG and prove it is a cellular complex.
Using this structure we generalize the topological (Bollobas-Riordan) Tutte
polynomials associated to (ribbon) graphs to topological polynomials adapted to
Colored Group Field Theory graphs in arbitrary dimension
- …