52,421 research outputs found
Low-lying zeros of L-functions for Quaternion Algebras
The density conjecture of Katz and Sarnak predicts that, for natural families
of L-functions, the distribution of zeros lying near the real axis is governed
by a group of symmetry. In the case of the universal family of automorphic
forms of bounded analytic conductor on a totally definite quaternion algebra,
we determine the associated distribution for a restricted class of test
functions. In particular it leads to non-trivial results on densities of
non-vanishing at the central point.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1810.0278
Primes in short intervals on curves over finite fields
We prove an analogue of the Prime Number Theorem for short intervals on a smooth projective geometrically irreducible curve of arbitrary genus over a finite field. A short interval “of size E” in this setting is any additive translate of the space of global sections of a sufficiently positive divisor E by a suitable rational function f. Our main theorem gives an asymptotic count of irreducible elements in short intervals on a curve in the “large q” limit, uniformly in f and E. This result provides a function field analogue of an unresolved short interval conjecture over number fields, and extends a theorem of Bary-Soroker, Rosenzweig, and the first author, which can be understood as an instance of our result for the special case of a divisor E supported at a single rational point on the projective line
Counting problems for geodesics on arithmetic hyperbolic surfaces
It is a longstanding problem to determine the precise relationship between
the geodesic length spectrum of a hyperbolic manifold and its commensurability
class. A well known result of Reid, for instance, shows that the geodesic
length spectrum of an arithmetic hyperbolic surface determines the surface's
commensurability class. It is known, however, that non-commensurable arithmetic
hyperbolic surfaces may share arbitrarily large portions of their length
spectra. In this paper we investigate this phenomenon and prove a number of
quantitative results about the maximum cardinality of a family of pairwise
non-commensurable arithmetic hyperbolic surfaces whose length spectra all
contain a fixed (finite) set of nonnegative real numbers
Quantum versus classical counting in nonMarkovian master equations
We discuss the description of full counting statistics in quantum transport
with a nonMarkovian master equation. We focus on differences arising from
whether charge is considered as a classical or a quantum degree of freedom.
These differences manifest themselves in the inhomogeneous term of the master
equation which describes initial correlations. We describe the influence on
current and in particular, the finite-frequency shotnoise. We illustrate these
ideas by studying transport through a quantum dot and give results that include
both sequential and cotunneling processes. Importantly, the noise spectra
derived from the classical description are essentially frequency-independent
and all quantum noise effects are absent. These effects are fully recovered
when charge is considered as a quantum degree of freedom.Comment: 12 pages; 3 figure
Segmentation algorithm for non-stationary compound Poisson processes
We introduce an algorithm for the segmentation of a class of regime switching
processes. The segmentation algorithm is a non parametric statistical method
able to identify the regimes (patches) of the time series. The process is
composed of consecutive patches of variable length, each patch being described
by a stationary compound Poisson process, i.e. a Poisson process where each
count is associated to a fluctuating signal. The parameters of the process are
different in each patch and therefore the time series is non stationary. Our
method is a generalization of the algorithm introduced by Bernaola-Galvan, et
al., Phys. Rev. Lett., 87, 168105 (2001). We show that the new algorithm
outperforms the original one for regime switching compound Poisson processes.
As an application we use the algorithm to segment the time series of the
inventory of market members of the London Stock Exchange and we observe that
our method finds almost three times more patches than the original one.Comment: 11 pages, 11 figure
Multiple time scale blinking in InAs quantum dot single-photon sources
We use photon correlation measurements to study blinking in single,
epitaxially-grown self-assembled InAs quantum dots situated in circular Bragg
grating and microdisk cavities. The normalized second-order correlation
function g(2)(\tau) is studied across eleven orders of magnitude in time, and
shows signatures of blinking over timescales ranging from tens of nanoseconds
to tens of milliseconds. The g(2)(\tau) data is fit to a multi-level system
rate equation model that includes multiple non-radiating (dark) states, from
which radiative quantum yields significantly less than 1 are obtained. This
behavior is observed even in situations for which a direct histogramming
analysis of the emission time-trace data produces inconclusive results
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