Math Colloquium: Masato Wakayama (Kyushu University)

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

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.

Event Sponsor
Mathematics , Mānoa Campus

More Information
956-7171

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