Seminar: Bohr-Sommerfeld rules for matrix-valued operators

Time:

Venue/Location: Phòng C101, VIASM

Báo cáo viên: Setsuro Fujiié, Ritsumeikan University, Japan

Tóm tắt: Bohr-Sommerfeld quantization rule is well known as the condition satisfied in the semiclassical limit by eigenvalues of the 1D Schrödinger operator with a single potential well. The single well makes a simple closed characteristic curve in the phase space, and the BohrSommerfeld rule reads where is the spectral parameter and is the volume of the domain bounded by this curve. The phase shift is the so-called Maslov correction. We generalize this rule to matrix-valued pseudo-differential operators, including varoius Dirac operators. In such matrix cases, the Bohr-Sommerfeld quantization rule is not always valid and some other corrections than the Maslov one are needed. We will give a geometric formula for these corrections. This is a joint work with Simon Becker and Jens Wittsten.