Colloquium- Masato Wakayama (Kyushu U.)

When:
September 5, 2014 @ 2:00 pm – 3:00 pm
2014-09-05T14:00:00-10:00
2014-09-05T15:00:00-10:00
Where:
Keller 301

Speaker: Masato Wakayama (IMI Kyushu U.)

Title: Quantum Rabi’s model and non-commutative harmonic oscillators – between
physics and number theory

Abstract: The quantum Rabi model is known to be the simplest model used in quantum optics to describe interaction of light and matter beyond the harmonic
oscillator. Although this model has had an impressive impact on many
fields of physics, only recently in 2011 could this model be declared
solved by D. Braak. Introduced over 70 years ago, its applications range
from quantum optics, magnetic resonance to solid state and molecular
physics. The non-commutative harmonics oscillator (NcHO) is a self-
adjoint, parity-preserving ordinary differential operator of order two
with non-commutative coefficient. The NcHO was introduced purely in
mathematics context in 1999. Although its spectrum is not still very
clear, the deep number theoretic properties of the spectral zeta
function shows the family of NcHOs has rich mathematical structure and
that’s why finding out an inter connection via representation theory
between NcHOs and Rabi -kind models would be interesting in both
mathematics and physics. In this talk, a non-trivial relation between
the quantum Rabi model and the NcHO discovered recently from the
representation theoretic viewpoint in terms of their Heun ODE pictures
will be given. Further, some number theoretical results, which may
relate to the Rabi model, will be also discussed.