Course Overview

Building on the foundation given in Statistical Mechanics I, this lecture introduces the path-integral formulation of the density matrix and discusses its applications to interacting many-body systems. The subjects include cluster expansion of gases and order-disorder phase transitions.

Learning Achievement

understand Feynman's path integral method and know how to apply it to specific statistical mechanics problems.

Competence

1. Basic engineering skills, 2, basic academic skills, 3. specialized knowledge, 4. practical insight and problem-solving skills.

Course prerequisites

Students should take Statistical Mechanics I , II, and III in order.

Grading Philosophy

Grading will be based on the final report (answers to questions).

Course schedule

Based on the content of Statistical Mechanics I, a path integral formulation of the density matrix is introduced and applied to interacting many-particle systems, with applications to cluster expansion of gas particles and order-disorder transitions.
Formulation and calculation with path integrals and density matrices
Path integrals and its application (free particles, harmonic oscillators)
Path integrals: perturbative expansions, variational principle
Applications of variational principle
Many-body system: Classical N-particle systems
Equation of State: The Second Virial coefficient
One-dimension gas: Born-Green equation
Order-disorder transition: 2-D lattices
2-dimension problem: Approximate solution
Onsager Problem: 2-D lattices

Course type

Lectures

Online Course Requirement

Instructor

Tong Xiao-Min,Hino Ken-ichi

Other information

Site for Inquiry

Link to the syllabus provided by the university