Graduate Level Statistical Physics I

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Nov 15, 2013 (3 years and 7 months ago)

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Syllabus

(subject to

changes)


Graduate Level

Statistical Physics I



First semester 2008
, School of Physics Tel Aviv University


Lecturer:
Eshel Ben
-
Jacob


Teaching assistance
:
Guy Ron


10+1

weeks
:

3
hours
frontal lectures and
1 hour Exercise lectur
e

per week

Lectures:

Wednesday 17:00
-
19:00 Melamed
lecture hall

06

Thursday


17:00
-
18
:00 Melamed lecture hall

06

Tirgulim:
Thursday


18:00
-
19
:00 Melamed lecture hall

06



Relevant material can be found in Ben
-
Jacob home page
http://star.tau.ac.il/~eshel/


Ben
-
Jacob’s emails
eshelbj@gmail.com



Ron’s Emai
l
s

ronguy@tauphy.tau.ac.il

ronguy@muon.tau.ac.il



Topics that will not be covered in 2008

are marked


Chapter 1: Concise review of thermodynamics (2 weeks)


Extensive and intensive variables, Equilibrium and the Ergodic theorem,
the E
ntropy a
nd
the Fundamental Equation
,
Eu
ler’s relations, and the thermodynamic potentials (Free
energies), Thermodynamic machines, Maxwell’s relations,
Maxwell demon, Szilard’s
and Brillion’s interpretations,

Einstein’s interpretation
of Planck equation and
and
photons,
Schrodinger’s negative en
tropy criteria.



Tutorial will include: Complete differentials, partial derivatives relations, Legendre’s
transformation, Black body radiation


Bibliography: Distributed notes,
Ben
-
Jacob’s book (Hebrew), The
Open University

course
, H.B. Callen, "Thermo
dynamics and an Introduction to Thermostatistics," 2d ed.,
Wiley (1985).



Chapter 2: The foundations of Statistical Physics (4 weeks)


The fundamental assumption: the
micro
-
level


macro
-
level relations, the notion of the
number of microscopic states, the

notion of the ensembles,
The connection with the
thermodynamic potentials,
The Micro
-
canonic and the Canonic ensembles, the chemical
potential and the Grand
-
canonic ensemble,
classical ideal gas and the Maxwell
distribution, Ideal gas of fermions and the
Fermi
-
Dirac distribution, Ideal gas of bosons
and the Bose
-
Einstein distribution, Bose
-
Einstein condensation an super
-
fluidity, Super
-
conductivity, Cold atoms.



Tutorial will include: the heat capacity of electrons in solids, heat capacity of phonons,

black body radiation revisited.


Bibliography: Distributed notes,
R.K. Pathria,
Statistical Mechanics
, 2nd
Edition,

and
`Statistical Mechanics' by S.K. Ma (World Scientific 1985)


Chapter 3: Phase transitions and
critical phenomena (3

weeks)


First and se
cond order phase transitions, Ising model, Mean Field Theory and landau
Theory, Coarse graining and Scaling, Critical exponent, Universality,
Renormalization
Group
, Correlations,
finite
-
size scaling
, Spin
-
glass and Frustration
.


Tutorial will include: Isin
g in two dimensions, Potss model, the X
-
Y model, Spin
-
glass
,
Metropolis and Monte
-
Carlo simulations,


Bibliography:

N. Goldenfeld,
Lectures on Phase Transitions and the Renormalization
Group

(Addison
-
Wesley, Reading, 1992) and P. M. Chaikin and T. C. Lube
nsky,
Principles of Condensed Matter Physics

(Cambridge University Press, Cambridge, 1995)


Chapter 4:
Time dependent phenomena (
Stochastic processes
) (2

weeks)


Fluctuations and noise (white noise, colored noise and shot noise), Random walk, the
Langevin

equation, Einstein’s Fluctuation
-
dissipation relations, the Diffusion equation,
the Fokker
-
Planck equation,
Kramer
s

activation theory
.


Tutorial will include:
Levy walk and Levy distribution, 1/f noise and fractals,
Phase
-
space and the Liouville equation
,

the Master equation, solutions of the Fokker
-
Planck
equation for special cases.



Bibliography:

Distributed notes,
N. G. Van Kampen
Stochastic Processes in Physics and
Chemistry

and H. Risken
The Fokker
-
Planck Equation: Methods of Solutions and
Applicatio
ns
, and also can be interesting to look at `Theory of the Brownian Movement'
by A. Einstein



Chapter 5: Advanced topics

(2 weeks)

-



Thermodynamics of Black Holes (B
ekenstein

entropy and Hawking radiation),
Polymers
entropy, membranes fluctuations, Prote
in folding, the properties of water, self
-
organization and pattern formation, inf
ormation theory.

Bibliography: `Equilibrium Statistical Physics', 2nd edition, by M. Plischke and B.
Bergersen, and we will distribute a list of links like the one below.

Information in the
Holographic Universe


Information in the
Holographic Universe
; August 2003;
Scientific American

Magazine; b
y
Jacob D.
Bekenstein
; 8 Page(s). Ask anybody what the physical world
...

www.sciamdigital.com/index.cfm?fa=Products.ViewIssuePreview&ARTICLEID_CHAR=4D0EEDA
F
-
DEB7
-
FC61
-
90CF673...
-

15k
-

Cached

-

Similar

pages




Additional References and links

`Statistical Mechanics', by L.D. Landau and E.M. Lifshitz (Pergamon)
-

a
really good
book, with many of the classical topics that we will discuss beautifully presented.


E ven
the old edition (one volume) is good.


Newer edition is split into two volumes; the second
volume is not needed for this course.


`Thermal Physics', Sec
ond Edition, by C. Kittel and H. Kroemer (Freeman and Co, New
York 1984).

Kittel wrote the first edition of this, in 1969, and Kroemer co
-
authored the
second edition, in 1980. (This is the same Herbert Kroemer that won the Nobel Prize in
2000.) This has be
en a very widely used

book for the last twenty years.

It deals almost
exclusively with statistical mechanics, with one chapter that derives the laws of
thermodynamics. The methods used to derive the statistical distribution laws were very
novel when the fi
rst edition was published, quite different from the counting techniques
used in the earlier books. For me, this is still slightly controversial. The problems at the
ends of chapters are excellent.

D. Chandler, "Introduction to Modern Statistical Mechanics"

Oxford University Press
(1987).

Leo P. Kadanoff,
Statistical Physics: Statics, Dynamics and Renormalization

(World
Scientific, Singapore, 2000)



Lecture Notes

in Statistical Mechanics


The
Renorma
lization
-
Group

Methods; Momentum
-
Space
Renormalization Group
.
Appendices. Further Reading; Distribution Functions; Maxwell Relations
...

www
-
f1.ijs.si/~vilfan/SM/cont.html
-

2k
-

Cached

-

Similar

pages



More advanced oldies

Kittel and Kro
emer

"Thermal Physics". Kittel wrote the first edition of this, in
1969, and Kroemer co
-
authored the second edition, in 1980. (This is the same
Herbert Kroemer that won the Nobel Prize in 2000.) This has been a very widely
used book for the last twenty yea
rs, although last year the book store told me it was
out of print. It deals almost exclusively with statistical mechanics, with one chapter
that derives the laws of thermodynamics. The methods used to derive the statistical
distribution laws were very nove
l when the first edition was published, quite
different from the counting techniques used in the earlier books. For me, this is still
slightly controversial. The problems at the ends of chapters are excellent.

Stowe

"Statistical Mechanics and Thermodynamic
s". I am less familiar with this
than any of the other books listed. It appeared in 1984. In some ways it follows the
conventional format, treating Classical Thermodynamics and then Statistical
Mechanics, but, before any of this there is a discussion of sm
all systems and ideas
from statistics, and the treatment of thermodynamics makes use of these ideas
rather than taking a purely macroscopic approach. One reason for looking at it is
that Dan Schroeder (see below) credits it as one of his inspirations.


The

New Wave

For some reason, there was a dearth of new books on thermal physics in the 1980's
and 1990's. Perhaps we all assumed that the last word had been written. For many
years, I used Zemansky for the first semester and Kittel and Kroemer for the
second
. Then there was a flurry of new books. Three appeared in 1999, and 2000,
and more are rumored. One characteristic of the new books is that they are tailored
to a one semester course on thermal physics, but all the authors try to do justice to
both sets of

ideas.

Schroeder

"Thermal Physics". Written in a very chatty style, that I wish I had
thought of. There is an immense number of problems, embedded in the text rather
than left to the chapter ends. The way to use this book seems clearly to work a lot of
pr
oblems as you go. Schroeder says that there is too much material for one
semester, but that it is still primarily intended for a one semester course. The
presentation starts with microscopic ideas, and freely mixes up microscopic and
macroscopic concepts a
ll the way through

Baierlein

"Thermal Physics" (there seem to be more new books than new titles).
This has much in common with Schroeder. It uses microscopic ideas to motivate and
justify the second law. But its treatment both of thermodynamics and statist
ical
mechanics is more formal that Schroeder's. (e.g. there is a chapter called "The
Canonical Probability Distribution". Schroeder buries the word "canonical" in a
footnote.) However, the treatment of Classical Thermodynamics does not follow the
tradition
al approach through heat engines, and the treatment of the probability
distributions follows Kittel and Kroemer's methods rather than, for example, Reif's
or Crawford's.

Carter

"Classical and Statistical Thermodynamics". This is by far the most
traditional

of the new books. It follows the pattern of Crawford and of Morse,
developing Classical Thermodynamics using a macroscopic approach, and then
Statistical Mechanics using the traditional Lagrange multiplier techniques.
However, Carter says that you can cov
er all of this in one semester.