Solution of the homework 1 for PHY 504 Statistical Physics
1, The methematical knowledge tells us the number
of different configurations for N up spin and N down spin is
N!
g HN, EL =
N ! N !
The task reduces to calculate what N and N are. It is not hard
Phy 504 hw 2 solution
February 26, 2013
1)(5) The spacing of particles should be larger than the characteristic length
h
2 mkT
(1)
N
1
<3
V
(2)
=p
so
n=
in the classical limit h ! 0 or at high temperature, the thermal wavelength becomes small
compared to
Phy 504 hw 4 solution
March 27, 2013
1
The Mayer Linked Cluster Expansion
1, The Grand Canonical Ensemble is
1
X
Z (, V, T ) =
z N Z (N, V, T )
(1)
N =0
Therefore the mean particle number is
P1
N
N =0 N z Z
h N i = P1
N
N =0 z Z
@ ln Z
=
@ ln z
The z = e
Phy 504 hw 5 solution
I.
STATISTICAL MECHANICS OF A GAS OF PHOTONS
1, Suppose ns (k ) is the number of photons with k and polarization s, then the partition
function is
X
Z=
X
~! ( k ) n s ( k ) + E 0
1
exp
e
k,s
cfw_ n s (k )
= exp(
E0 )
Y
k,s
!
1
(1)
~
Phys 504 hw 6 solution
I.
THE ONE DIMENSIONAL CLASSICAL ISING MODEL
1,
Z=
=
X
E[ ]
e
N
XY
exp( J
i i+1
+ H i)
i=1
= tr(
N
Y
exp(
i i+1
H
(
2
+
i=1
Let h i |T | j i = exp( J
ij
+
H
(i
2
+
i
+
i+1 )
i+1 )
Then
Z = tr[h 1 |T | 2 ih 2 |T | 3 i h
N |T
1 i]
= t