Dykhne–Davis–Pechukas (DDP) method is a common approximation scheme for the transition probability in two-level quantum systems, as realized in the Landau–Zener effect, leading to an exponentially damping form comparable to the Schwinger pair production rate. We analyze the foundation of the DDP method using a modern complex technique inspired by the Lefschetz-thimble method. We derive an alternative and more adaptive formula that is useful even when the DDP method is inapplicable. As a benchmark, we study the modified Landau–Zener model and compare results from the DDP and our methods. We then revisit a derivation of the Schwinger Mechanism of particle production under electric fields using the DDP and our methods. We find that the DDP method gets worse for the Sauter type of short-lived electric pulse, while our method is still a reasonable approximation. We also study the Dynamically Assisted Schwinger Mechanism in two methods.

学問の世界で大切なのは、研究者の「なぜ」「不思議だな」という好奇心です。研究者は自らの好奇心をもとに想像力を膨らませ、さまざまな仮説を立て、それを実験、観測、調査で検証し、最終的には理論的に体系づけていきます。このような基礎研究で得られた知識は、私たちの生活に直接「役に立つ」ものではありません。しかし、5年、10年といった期間ではなく、100年、1000年単位で考えると、基礎研究は確実に世の中の役に立ち、私たちはその恩恵にあずかっています。

現在、国内外の大学や研究機関には、企業の経営戦略からきている「選択と集中」の考えが入ってきており、好奇心に基づいた研究を進めることが難しくなっています。令和時代において、私たちはどのように基礎研究を継続させていくことができるのでしょうか。今回のイベントでは、各分野で活躍する3名の研究者にお越しいただき、登壇者の一人でもある初田哲男氏監訳の書籍タイトル『「役に立たない」科学が役に立つ』をテーマとした議論を進めていきます。

13:00-13:05　Opening
13:05-14:05　Topics
14:10-15:20　Panel Discussion
15:20-15:30　Summary

Capacity: 1,000 people
Participation fee: Free of charge
Target audience: everyone is welcome to attend
Organized by iTHEMS and Academist

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This is a series of lectures on "Geometric Perspectives for Fluid Dynamic Limit Theory" by the following speakers:
[DAY 1: Aug 31] Dr. Makiko Sasada (University of Tokyo)
[DAY 2: Sept 1] Prof. Kenichi Bannai (Keio University)

Abstract:
One of the fundamental problems in the natural and social sciences is to explain macroscopic phenomena that we can observe from the rules governing the microscopic system giving rise to the phenomena. Hydrodynamic limit provides a rigorous mathematical method to derive the deterministic partial differential equations describing the time evolution of macroscopic parameters, from the stochastic dynamics of a microscopic large scale interacting system.

In the article "Topological Structures of Large Scale Interacting Systems via Uniform Locality" joint with Yukio Kametani, we introduce a general framework encompassing a wide variety of interacting systems in order to systematically investigate various microscopic stochastic large scale interacting systems in a unified fashion. In particular, we introduced a new cohomology theory called the uniformly local cohomology to investigate the underlying geometry of the interacting system. Our theory gives a new interpretation of the macroscopic parameters, the role played by the group action on the microscopic system, and the origin of the diffusion matrix associated to the macroscopic deterministic partial differential equation obtained via the space-time scaling limit of the microscopic system.

The purpose of the series of lectures is to introduce to the audience the theory of hydrodynamic limits, especially the relation between the macroscopic observables and the microscopic interacting system. We then explain our new perspective of how geometry comes into play in investigating the interacting system, and introduce the ideas and results of our article.

*Detailed information about the seminar refer to the email.