Frédéric Klopp (Paris-Jussieu)
Stark-Wannier ladders and cubic exponential sums
The talk is devoted to Stark-Wannier ladders i.e. the
resonances of a one dimensional periodic operator in a
constant electric field. The periodic sequences of points in
the lower half of the complex plane have been conjecture to be
very sensitive to the nulmber theoretical properties of the
electric field. Computing the asymptotics of the reflection
coefficients in the case of simple 1-periodic potential, we
related the resonances to cubic exponential sums in which the
frequency is computed from the electric field. In the case of
rational frequency, we derive "large imarginary part"
asymptotics for the resonances.
The talk is based on joint work with A. Fedotov (St Petersburg).