Deriving stochastic crystal model from Hamiltonian dynamical system and the effect of relative effecacy

2016 Fiscal Year Final Research Report

• Project/Area Number: 25800056
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: University of Tsukuba
• Principal Investigator: LIANG Song 筑波大学, 数理物質系, 准教授 (60324399)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 拡散過程 / 確率微分方程式 / 古典力学系 / 収束

Outline of Final Research Achievements

Put two heavy particles into an ideal gas environment, a system consists of infinitely many light particles with a certain initial distribution, and assume that the interactions between particles are non-random. In this research, the interactions between the heavy particles and the light particles are assumed to be of same type. We are interested in the problem of the limit behaviors of the heavy particles when the mass of the light particles converges to 0, under different settings.
We considered the stochastic differential equations corresponding to the cases with or without relative efficacy for the behaviors of heavy particles, and proved the convergences of the corresponding stochastic processes. This gives us the concrete expressions of the only candidate limit processes for each case. Also, we proved the convergence of the particle-environment model to this candidate for the case with relative efficacy.

Free Research Field

確率論