11 research outputs found
Existence of the Stark-Wannier quantum resonances
In this paper we prove the existence of the Stark-Wannier quantum resonances
for one-dimensional Schrodinger operators with smooth periodic potential and
small external homogeneous electric field. Such a result extends the existence
result previously obtained in the case of periodic potentials with a finite
number of open gaps.Comment: 30 pages, 1 figur
A central limit theorem for the zeroes of the zeta function
On the assumption of the Riemann hypothesis, we generalize a central limit
theorem of Fujii regarding the number of zeroes of Riemann's zeta function that
lie in a mesoscopic interval. The result mirrors results of Soshnikov and
others in random matrix theory. In an appendix we put forward some general
theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.Comment: 22 pages. Incorporates referees suggestions. Contains minor
corrections to published versio