|
Home
Overview
Instructors
Course Info
Communications
Calendar
Unit Topics
Notes
Videos
Problem Sets
Zoom
Email
Discussion
Slack
|
|
|
|
PHY 418: Statistical Mechanics I
Prof. S. Teitel: stte@pas.rochester.edu ---- Spring 2021
Problem Set 12
No Discussion Question this week!!
Problems -- Due Thursday, May 6, by 5pm.
Upload your solutions to Blackboard at this link: PS12
- Problem 1 [20 points]
N fermions A of spin 1/2 (i.e. gs=2) are introduced into a large volume V at
temperature T. Two fermions may combine to create one boson with
spin 0 (i.e. gs=1) via the interaction,
A + A ↔ A2
Creation of the molecule A2 costs energy εo > 0.
At equilibrium, the system will contain NF fermions and
NB bosons. Provide expressions from which the ratio
NB/NF can be calculated, and perform the
calculation explicitly for T=0. What would this (T=0) ratio be,
if the particles were classical (i.e. quantum statistics could be neglected).
Explain the difference.
- Problem 2 [10 points]
Consider the Ising model. The magnitization density is m, and the magnetic field is h. The magnetic susceptibility is then defined by
where the derivative is evaluated at h = 0.
Derive an expression for χ in terms of the fluctuations in magnetization m.
(Hint: recall, we had a similar expression for specific heat in terms of fluctuations in energy, and for compressibility in terms of fluctuations in volume.)
Show from this result that fluctuations in magnetization become negligible in the thermodynamic limit, except at a critical point.
|
|