Quantum evolution in a magnetic field and the tail behaviour of Weyl sums
speaker: Francesco Cellarosi (Queen's University)abstract: We will discuss the time evolution of a “box” function according to the Schrödinger equation in the presence of a magnetic field. This problem naturally leads to the study of a 1-parameter family of integral operators, interpolating between the identity and the Fourier transform. We provide an asymptotic estimate for the L-infinity norm of these Fourier-like multipliers when the box is approximated by slightly more regular functions as the size of the approximation tends to zero. As an application, we obtain an improved bound for the tail of the limiting distribution arising from quadratic Weyl sums. Their limiting distribution is obtained using homogeneous dynamics, along with a dynamical partition of unity, based on earlier work with J. Marklof. Joint work with J. Griffin and T. Osman.
timetable:
Tue 4 Jun, 15:00 - 15:45, Aula Dini
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