Gross-Pitaevskii theory of supersolids Part II

发布时间：2025-04-14 作者：浏览次数：

Speaker:	Professor Mathieu Lewin	DateTime:	Beijing Time: 15: 30--16: 30, April 15th (Tuesday), 2025; Paris Time: 9: 30--10:30, April 15th (Tuesday), 2025.
Brief Introduction to Speaker: Mathieu Lewin现为法国巴黎九大教授，2022年国际数学家大会45分钟报告人。主要从事数学物理、偏微分方程、变分理论等领域的理论研究，特别是在量子多体系统分析领域做出过具有国际影响力的系列研究成果，在Invent. Math.、Bullet. AMS、CPAM、Duke Math. J.、JEMS等国际顶尖数学期刊上发表论文90余篇，现为国际数学杂志AIH. Poincare-Analyse Non Lineaire主编，担任J. Spectral Theory、L. Math. Physics、Math. Models & Methods in Applied Sciences等国际数学期刊编委。		Place:	Zoom Meeting ID: 957 531 2886, Passcode: 202504
Abstract:We consider the stationary Gross-Pitaevskii equation for an extended function not tending to 0 at infinity, which describes the condensate part of an infinite Bose gas. The goal of the lecture will be to explain how to mix tools from PDEs and statistical mechanics to study the phase diagram of this model. In particular, we will prove that there is a unique freezing transition for interaction potentials that are stable but not positive definite. The conjecture is that the solutions in the solid phase are periodic. Those describe a supersolid, a state of matter that has been the subject of much recent experimental work. Work in collaboration with Phan Thành Nam (Munich).