Contact: Chris Bourne cbourne [at] nagoya-u.jp, bourne.christopher.jack.x7 [at] f.mail.nagoya-u.ac.jp
Office Hours: TBA
Location: Room 419, Humanities Common Facility Building (A4② on the Campus Map).
Registration code: 3211092
Time: Friday 10:30-12:00
Location: TBA
Syllabus: In preparation
Course outline: In preparation
October 2, 9, 16, 23, 30
November 6, 13, 27
December 4, 11 18, 25
January 8, 22, 29
February 5
Course title: Mathematical aspects of condensed matter physics
Condensed matter physics is a branch of quantum mechanics that studies the microscopic and macroscopic properties of solid and liquid phases of matter. The goal of the course is to introduce the mathematical theories that underpin condensed matter physics, including functional analysis, spectral theory and operator algebras, and understand their relevance to physical properties and phenomena.
講義のテーマ：物性物理学の数学的側面
物性物理学は，物質の固体相および液体相の性質を研究する量子力学の一分野である．本科目の目的は，関数解析，スペクトル理論，作用素環など，物性物理学の基礎となる数学的理論を概説し，それらが物理的性質や現象とどのように関連しているかを理解することである．
This course will be conducted in English. この講義を英語で行います．
For this topic, we will look at the mathematical aspects of condensed matter physics in the setting of lattice systems. For the first part, we will consider single-particle dynamics (free fermions) and the interaction between the spectrum of an operator with physical properties of the system. For the second part, we will introduce and study the elementary properties of quantum spin systems.
Lecture notes: In preparation
Outline (tentative):
Part 1: Quantum dynamics and the spectrum
- Introduction to single-particle quantum mechanics
- Locality and the Bloch decomposition/Fourier series
- Types of quantum motion and spectral type
- Linear response theory and the Kubo formula
- Topology and the integer quantum Hall effect
Part 2: Quantum spin systems
- Basics of quantum spin systems and the Heisenberg model
- Spontaneous symmetry breaking and long-range order
- Ground states and the Haldane conjecture
- Operator algebras and the infinite volume limit
Lecture notes by Jacob Shapiro.
Hal Tasaki. Physics and Mathematics of Quantum Many-Body Systems. Springer, 2020.
Walter Rudin. Real and Complex Analysis. McGraw-Hill Education, 1986.
Michael Reed and Barry Simon. Methods of Modern Mathematical Physics I: Functional Analysis. Academic Press Inc., 1980.
In preparation / 作成中