**↑**

** Fumio**

## DATE: October 23, 10:00 - October 24, 17:30, 2014

VENUE: Seminar Room 7, Faculty of Mathematics building /

IMI (Institute of Mathematics for Industry),

Ito Campus, Kyushu University

## NEW TOPICS

2014.08.13 | Program Up! Please go to PROGRAM. |
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2014.05.30 | Website Open! |

## SYNOPSIS

In the early 20th century Heisenberg's discovery of a rule showing
that the measurement of the position and momentum of quantum particle gives
different answers depend on the order of their measurement led to
canonical commutation relations, and it was the foundation of quantum
mechanics, which finds unexpected applications in the natural science.
Beyond the quantum mechanics Heisenberg and Pauli also discovered
quantum field theory in 1930's, which succeeded to describe quantum
electrodynamics (QED) and led to the standard model in 1970's.
In QED photon field can be realized as the correction of harmonic oscillators.
In 1936 I. I. Rabi introduced a model describing harmonic oscillators coupled
to 2 level atoms, which is the so-called quantum Rabi model nowadays.
At the time no one could expect to see single photon.
Surprisingly single photon however can be controlled in laboratories in the present day and the Rabi model has
gained a prominent role in cavity QED and circuit QED.

On the other hand from the pure mathematical point of view, Parmeggiani and Wakayama introduced the so called non-commutative harmonic oscillator (NCHO) which is defined by 1D harmonic oscillator with non- commutative coefficients coming from sl(2) representation in 1999. The spectrum of NCHO defines the spectral zeta function ζ

On the other hand from the pure mathematical point of view, Parmeggiani and Wakayama introduced the so called non-commutative harmonic oscillator (NCHO) which is defined by 1D harmonic oscillator with non- commutative coefficients coming from sl(2) representation in 1999. The spectrum of NCHO defines the spectral zeta function ζ

_{Q}(s) and recently the properties of ζ_{Q}(s) is studied from the viewpoint of number theory. It was also discovered relationships between the Rabi model and NCHO through the Heun differential equation by one of organizers of this workshop. The purpose of this workshop is to provide inspiring and pleasant environments to discuss the Rabi, NCHO and related topics without any boundary conditions to all the participants in the best season in Fukuoka. Enjoy mathematics and physics!