Exactly solvable models in physics

Time and place: Mo. 10:00-12:00 / E2.6 Room 4.18
Starting: 2 May 2016
Lecturer: Dr. Chikashi Arita


  • On 23 May the lecture will take place as usual, but there will be no lecture on 30 May.


There exist exactly solvable models in non-linear differential equations, quantum systems and statistical mechanics. We shall study typical methods to solve these models. More specifically we shall treat the following topics. (Any background knowledge is not required.)

  • Non-linear equations and soliton theory
    • Duffing equation
    • Burgers equation, KdV equation
    • Toda lattice
    • Singular perturbation
    • Hirota’s method
    • Lax pair
  • Spin chains
    • Ising model
    • Heisenberg chains
    • Yang-Baxter equation and Bethe ansatz method
  • Stochastic processes
    • master equation and stationary state
    • detailed balance condition
    • scalar and matrix product forms