Joint ICTP/SISSA Statistical Physics seminar:
Series of lectures on: 'Singularities and asymptotics'
"Boundary-varying boundary conditions:
The Dirichlet singularity"
Starts 5 Jun 2008 16:00
Ends 5 Jun 2008 20:00
Central European Time
Leonardo da Vinci Building Lecture Room B
Strada Costiera, 11
I - 34151 Trieste (Italy)
Waves in a two-dimensional domain with Robin (mixed) boundary conditions that vary smoothly along the boundary exhibit unexpected phenomena. If the variation includes a ‘D point’ where the boundary condition is Dirichlet (vanishing wavefunction), the system is singular. For a circle billiard, the boundary condition fails to determine a discrete set of levels, so the spectrum is continuous. For a diffraction grating defined by periodically-varying boundary conditions on the edge of a half-plane, the phase of a diffracted beam amplitude remains undetermined. In both cases, the wavefunction on the boundary has a singularity at a D point, described by the polylogarithm function.
ICTP - Strada Costiera, 11
I - 34151 Trieste Italy (+39) 040 2240 111 email@example.com