160 research outputs found
On the convergence of the usual perturbative expansions
The study of the convergence of power series expansions of energy eigenvalues
for anharmonic oscillators in quantum mechanics differs from general
understanding, in the case of quasi-exactly solvable potentials. They provide
examples of expansions with finite radius and suggest techniques useful to
analyze more generic potentials.Comment: 11 pages, Latex (1 EPS figure included
Dilatation operator and Cayley graphs
We use the algebraic definition of the Dilatation operator provided by
Minahan, Zarembo, Beisert, Kristijansen, Staudacher, proper for single trace
products of scalar fields, at leading order in the large-N 't Hooft limit to
develop a new approach to the evaluation of the spectrum of the Dilatation
operator. We discover a vast number of exact sequences of eigenstates.Comment: 30 pages and 3 eps figures, v2: few typos correcte
Quartic Anharmonic Oscillator and Random Matrix Theory
In this paper the relationship between the problem of constructing the ground
state energy for the quantum quartic oscillator and the problem of computing
mean eigenvalue of large positively definite random hermitean matrices is
established. This relationship enables one to present several more or less
closed expressions for the oscillator energy. One of such expressions is given
in the form of simple recurrence relations derived by means of the method of
orthogonal polynomials which is one of the basic tools in the theory of random
matrices.Comment: 12 pages in Late
Non-universality of compact support probability distributions in random matrix theory
The two-point resolvent is calculated in the large-n limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with that of the canonical Gaussian ensemble by a nonuniversal part that is given explicitly for all monomial potentials V(M)=M2p. Moreover, we prove that for the generalized fixed and bounded trace ensemble all k-point resolvents agree in the large-n limit, despite their nonuniversality
Photonic gaps in cholesteric elastomers under deformation
Cholesteric liquid crystal elastomers have interesting and potentially very
useful photonic properties. In an ideal monodomain configuration of these
materials, one finds a Bragg-reflection of light in a narrow wavelength range
and a particular circular polarization. This is due to the periodic structure
of the material along one dimension. In many practical cases, the cholesteric
rubber possesses a sufficient degree of quenched disorder, which makes the
selective reflection broadband. We investigate experimentally the problem of
how the transmittance of light is affected by mechanical deformation of the
elastomer, and the relation to changes in liquid crystalline structure. We
explore a series of samples which have been synthesized with photonic stop-gaps
across the visible range. This allows us to compare results with detailed
theoretical predictions regarding the evolution of stop-gaps in cholesteric
elastomers
Real symmetric random matrices and paths counting
Exact evaluation of is here performed for real symmetric
matrices of arbitrary order , up to some integer , where the matrix
entries are independent identically distributed random variables, with an
arbitrary probability distribution.
These expectations are polynomials in the moments of the matrix entries ;
they provide useful information on the spectral density of the ensemble in the
large limit. They also are a straightforward tool to examine a variety of
rescalings of the entries in the large limit.Comment: 23 pages, 10 figures, revised pape
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