E XERCISES STATISTICAL MECHANICS , EXTRA
Consider a classical system of N identical particles, that is described by a Hamiltonian H . Assume that
we found an approximated Hamiltonian H0 , from which we can determine all statistical quantities.
E XERCISES STATISTICAL MECHANICS , WEEK 10
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 to a homogeneous magnetic eld H .
For small values of
E XERCISES STATISTICAL MECHANICS , WEEK 11
1. Landau-Ginzburg theory
The Landau-Ginzburg Hamiltonian is given by
[m(r)]2 + m2 (r) + um4 (r) .
For system of spins on a square lattice with lattice constant a, the gradient must be
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
Department of Applied Physics and DIMES, Delft University of Technology, Lorentzweg
E XERCISES STATISTICAL MECHANICS , WEEK 13
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) = mgq; de collissions at q = 0 and q = L are elastic.
E XERCISES STATISTICAL MECHANICS ,
1. Exercise 4.6.1 (High temperature expansion and Kramers-Wannier duality)
on the extra pages.
2. Relation between scattering cross section and structure factor
In this exercise we analyse the relation
E XERCISES STATISTICAL MECHANICS , WEEK 6
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 (xi x j ) =
for |xi x j | < a and
for |xi x j | > a.
E XERCISES STATISTICAL MECHANICS , WEEK 7
1. Van der Waals equation of state
Consider a gas whose equation of state is given by
(v b) = kT
where v is the specic volume, v = V /N . This is the equation of state of a van der Waals gas.
E XERCISES STATISTICAL MECHANICS , WEEK 8
1. Exercise 5.7.7 (Superuidity for Hardcore Bosons) on the extra pages.
2. Perturbation Theory for Liquids
In this exercise we will investigate the ideas on which the modern perturbation theories of