stochastic geometric approach to stochastic processes in non equilibrium statistical mechanics

2015 Fiscal Year Final Research Report

• Project/Area Number: 25610021
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: Hara Takashi 九州大学, 数理(科)学研究科(研究院), 教授 (20228620)
• Co-Investigator(Renkei-kenkyūsha): Tasaki Hal 学習院大学, 理学部, 教授 (50207015)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 統計力学 / 緩和時間 / 非平衡状態 / 量子力学 / マクロな物理量 / 確率過程 / 非平衡部分空間

Outline of Final Research Achievements

In our daily life, we experience various relaxation or thermalisation phenomena. A typical example will be that a cup of hot coffee becomes cooler until its temperature approaches that of our room. However, there seems to be no satisfactory theory which can explain these phenomena starting from quantum mechanics.
In this research, we tried to find out general conditions under which relaxation occurs, and also tried to estimate relaxation time scales.
We have shown that under a "natural" assumption (non-equilibrium subspace is "typical"), relaxations do always occur, but that the relaxation time scale is extremely small (about poco seconds, called "Boltzmann time"). Our result suggests that the "natural" assumption about relaxation is not natural at all, and relaxation phenomena are more complicated than we first thought.

Free Research Field

数理物理学，確率論，統計力学