229 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
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
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
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
Shearing or Compressing a Soft Glass in 2D: Time-concentration superposition
We report surface shear rheological measurements on dense insoluble
monolayers of micron sized colloidal spheres at the oil/water interface and of
the protein -lactoglobulin at the air/water surface. As expected, the
elastic modulus shows a changing character in the response, from a viscous
liquid towards an elastic solid as the concentration is increased, and a change
from elastic to viscous as the shear frequency is increased. Surprisingly,
above a critical packing fraction, the complex elastic modulus curves measured
at different concentrations can be superposed to form a master curve, by
rescaling the frequency and the magnitude of the modulus. This provides a
powerful tool for the extrapolation of the material response function outside
the experimentally accessible frequency range. The results are discussed in
relation to recent experiments on bulk systems, and indicate that these two
dimensional monolayers should be regarded as being close to a soft glass state.Comment: to appear in PR
- …