제 2 회 수학자를 위한 통계역학 겨울학교
1월 18일-20일, 2021년
Online via Zoom (1월 15일까지 등록하신 분들께 Zoom 링크를 보내드립니다)

지난번 "수학자를 위한 열역학/통계역학" 강의에서 미진했던 부분을 보완하기 위해 두번째 온라인 모임을 준비하였습니다. 이번에는 두 분의 연사(백용주(서울대 물리천문), 유현재(한경대 응용수학) 교수님) 들이 모두 Zoom을 통해 강연을 해주시기로 하였습니다.

일정:
1월 18일 오전 10시 - 12시 + 오후 2시 - 4시 (연사 백용주)
1월 19일 오후 2시 - 4시 (연사 유현재)
1월 20일 오후 2시 - 4시 (연사 유현재)

참가에 관심있는 분들은 이훈희(E-mail: hunheelee_at_snu_dot_ac_kr)에게 메일로 문의바랍니다.

강연안내

백용주 (서울대, 물리천문학부) Introduction to statistical mechanics

초록: Using probabilities to account for the effects of uncontrolled or unobservable variables, statistical mechanics bridges the gap between microscopic and macroscopic physics. This lecture is an introduction to the theoretical framework and basic applications of equilibrium statistical mechanics, covering the following topics:

1. Thermodynamic ensembles

- Derivations from the fundamental postulate of statistical mechanics

- Principle of maximum entropy: an alternative Bayesian perspective

- Ensemble equivalence

2. Classical Boltzmann statistics

- Classical ideal gas

- Equipartition theorem

3. Quantum statistics

- Fermi-Dirac statistics

- Bose-Einstein statistics

4. Phase transitions

- Liquid-gas phase transition

- Ising model

유현재 (한경대, 응용수학과) Statistical mechanics: from the mathematical viewpoints

초록: In these lectures we discuss the statistical mechanics from the mathematical viewpoints. Specifically, we focus on the lattice models. Typical examples are the Ising model and the lattice gas model. The lectures are focused on: 1. Characterization of Gibbs measures, 2. Phase transitions, 3. Some applications. In the first two lectures we will discuss the Gibbs measures. Given an interaction, the equilibrium states, or the Gibbs measures, for the interaction are characterized in a couple of (equivalent) ways. Analytically, a Gibbs measure is characterized by tangent functionals to a (convex) function, the pressure. The variational principle is also a key tool to analyze the Gibbs measures. Rather probabilistically, the Gibbs measures are defined to be the measures that satisfy the DLR (Dobrushin-Lanford-Rulle) conditions. Vaguely speaking, it says that if you take a conditional expectation of the ‘equilibrium measure’ to any sub-sigma-algebra on the outside of a local system, the inside has a density of Boltzmann factor. In the 3rd lecture, we will discuss the phase transitions through symmetry breaking. In the final lecture, we will discuss some of the applications of the Gibbs measures.

강의노트 다운로드
Organizing Committee: 이훈희(서울대)
후원: 한국연구재단