Prof. Takuma Akimoto

Date: Feb. 7th, 17:00-

Title: Infinite ergodic theory in non-stationary stochastic processes with application to subrecoil laser cooling

Abstract:

Subrecoil laser cooling is a powerful technique to cool atoms beyond recoil limit [1]. This cooling technique can be realized by constructing the heterogeneous environment on the momentum space, where the dynamics of the momentum of an atom are modeled by a heterogeneous random walk (HRW) [2]. In our previous study [3], we considered the uniform approximation for the jump distribution of the momentum in the HRW model (exponential model) and solved the master equation. Since the cooling process is essentially non-stationary, there is no steady-state in the momentum distribution. In fact, the formal steady-state distribution for the master equation cannot be normalized. This unnormalized distribution is called an infinite invariant measure in ergodic theory [4]. In this talk, I will review the infinite ergodic theory and show how the tools in infinite ergodic theory can be applied to physical phenomena such as subrecoil laser cooling. I will report that the integrability of the observable with respect to the infinite invariant measure plays an important role in obtaining the ergodic properties. I will discuss the general validity of the infinite ergodic theory in non-stationary phenomena.