UNIVERSITY OF SURREY
DEPARTMENT OF PHYSICS
Level 2 Classical Laboratory Experiment
THE CURRENT BALANCE (CURRENT)
How to measure o , the magnetic permeability of free space
In this 2-week experiment you will study the force between pa
Physics 211 HER-"#1 Solution
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1. Derive the analogous (you have to gure out what analogous
means) equation of Eq.(2.5) for the ensemble where the energy,
and volume are not xed.
2. An ideal gas is held at temperature T in a cubic box of volume
V . Let the pressure of the gas be p. N
Consider the one dimensional Neite Ising model in the form of a.
H = JZ Ji'j
where o = :|:1.
(a) Show that the partition function is given by
z = Tr (TN)
T Bar EIer
= _,3.r ,3; (b) Determine the free energy per site
as N > 0
1. In class we derived the critical exponent (from the mean-eld
theory) by considering T > Tc . Do the same for T < Tc . For
T < Tc the susceptibility is dened as
(m(h, T ) m0 (T )|h0 ,
where m0 (T ) is the spontaneous magnetization.
2. Start from t
Elaboration of 4.5.2
Part I: Fourier Transforming the Hamiltonian
Let us begin with the continuum limit Hamiltonian:
dd x |
S |2 .
Since we are only interested in a net divergence, we shall aggressively drop constants all
1. Consider a neutron star with mass M = 3M . Estimate it size,
and calculate the neutron Fermi energy.
2. The low energy Hamiltonian of graphene is
HK = x px + y py HK = x px y py ,
, y =
Neutral graphene must have equal num
1. Prove that the Hemholtz free energy of Fermi gas obeys the following scaling law
F (T, N, V ) = N
F S1 (kB T / F ).
2. Compute the rst three terms of the power series expansion of
3. Show that the equation of states of the free Fermi gas obey
1. Suppose we place a three dimensional Bose gas under a external
V (x; y; z) =
(x + y 2 + z 2 ).
Calculate the Critical temperature and condensate fraction as a
function of temperature.
2. Consider a Bose gas where each Bose atom has tw
Nowadays the cold atom community is interested in simulating
lattice models by using laser to trap cold atoms so that they form a
lattice. A particular problem of interest is the antiferromagnetic phase
of the Mott insulating state of the two dimensiona