E XERCISES STATISTICAL MECHANICS , EXTRA
AUTUMN 2007
Consider a classical system of N identical particles, that is described by a Hamiltonian H . Assume that
we found an approximated Hamiltonian H0 ,
E XERCISES STATISTICAL MECHANICS , WEEK 10
AUTUMN 2007
1. Exercise 3.14 (Alben model)
on the extra page.
2. Phase transitions in a magnetic system
A magnetic system with magnetization m can be subject
E XERCISES STATISTICAL MECHANICS , WEEK 11
AUTUMN 2007
1. Landau-Ginzburg theory
The Landau-Ginzburg Hamiltonian is given by
H =
r
K
r
[m(r)]2 + m2 (r) + um4 (r) .
2
2
For system of spins on a square
VOLUME 84, NUMBER 13
PHYSICAL REVIEW LETTERS
27 MARCH 2000
High-Field Electrical Transport in Single-Wall Carbon Nanotubes
Zhen Yao,1 Charles L. Kane,2 and Cees Dekker1
1
Department of Applied Physics
E XERCISES STATISTICAL MECHANICS , WEEK 13
AUTUMN 2007
1. Bolzmann Equation
A particle with mass m, that can only move in a straight line 0 q L , experiences a gravitational force with potential V (q)
E XERCISES STATISTICAL MECHANICS ,
AUTUMN 2007
WEEK
8
1. Exercise 4.6.1 (High temperature expansion and Kramers-Wannier duality)
on the extra pages.
2. Relation between scattering cross section and st
E XERCISES STATISTICAL MECHANICS , WEEK 6
AUTUMN 2007
1. Tonks Gas
Consider a one dimensional gas of particles of length a conned to a strip of length L. The
particles interact through the potential
U
E XERCISES STATISTICAL MECHANICS , WEEK 7
AUTUMN 2007
1. Van der Waals equation of state
Consider a gas whose equation of state is given by
P+
a
(v b) = kT
v2
where v is the specic volume, v = V /N .
E XERCISES STATISTICAL MECHANICS , WEEK 8
AUTUMN 2007
1. Exercise 5.7.7 (Superuidity for Hardcore Bosons) on the extra pages.
2. Perturbation Theory for Liquids
In this exercise we will investigate th