207,776 research outputs found
Periodic-Orbit Theory of Anderson Localization on Graphs
We present the first quantum system where Anderson localization is completely
described within periodic-orbit theory. The model is a quantum graph analogous
to an a-periodic Kronig-Penney model in one dimension. The exact expression for
the probability to return of an initially localized state is computed in terms
of classical trajectories. It saturates to a finite value due to localization,
while the diagonal approximation decays diffusively. Our theory is based on the
identification of families of isometric orbits. The coherent periodic-orbit
sums within these families, and the summation over all families are performed
analytically using advanced combinatorial methods.Comment: 4 pages, 3 figures, RevTe
Poincare Recurrences and Topological Diversity
Finite entropy thermal systems undergo Poincare recurrences. In the context
of field theory, this implies that at finite temperature, timelike two-point
functions will be quasi-periodic. In this note we attempt to reproduce this
behavior using the AdS/CFT correspondence by studying the correlator of a
massive scalar field in the bulk. We evaluate the correlator by summing over
all the SL(2,Z) images of the BTZ spacetime. We show that all the terms in this
sum receive large corrections after at certain critical time, and that the
result, even if convergent, is not quasi-periodic. We present several arguments
indicating that the periodicity will be very difficult to recover without an
exact re-summation, and discuss several toy models which illustrate this.
Finally, we consider the consequences for the information paradox.Comment: 18 + 8 pages, 5 figures. v2: reference adde
Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws
* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.In this paper a general theory of a random number of random variables
is constructed. A description of all random variables ν admitting an analog
of the Gaussian distribution under ν-summation, that is, the summation of a random
number ν of random terms, is given. The v-infinitely divisible distributions
are described for these ν-summations and finite estimates of the approximation of
ν-sum distributions with the help of v-accompanying infinitely divisible distributions
are given. The results include, in particular, the description of geometrically
infinitely divisible and geometrically stable distributions as well as their domains
of attraction
On asymptotic constancy for linear discrete summation equations
AbstractThis paper studies linear discrete summation equations, defined in terms of infinite matrices. Sufficient conditions are given for such equations to have solutions converging to a (finite) limit. Reliance is made on results from the theory of summability methods, including the Kojima–Schur theorem. An application is given to a discrete summation equation arising in time series
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