**Course:** *Methods of Statistical Physics* -- develops the basic
principles of equilibrium statistical mechanics and their application to the
thermodynamics of a wide variety of physical systems.

**Prerequisites:** *Phys 404* or equivalent. A reasonable mastery
of basic thermodynamics and quantum mechanics is assumed.

**Instructor: **James
J. Kelly Phone: 405-6110
e-mail:
jjkelly@physics.umd.edu

**Lectures:** TuTh 9:30 - 10:50
Room 4208

**Office hours:** W 10-12
Room 2215 C

Although I prefer that you use the scheduled office hours, I am often available at other times also. Please come frequently.

**Grader:** Prof. H.H. Chen
Phone: 5-6088 e-mail: hsinghenchen@yahoo.com

**Office hours:** F 9:00-12:00
Room 3102

**Required text: ***Statistical Mechanics,* by R.K. Pathria (Butterworth-Heinemann,
1966)

**Useful supplements:**

*Equilibrium Statistical Mechanics*, G.F. Mazenko (Wiley, 2000)*Thermodynamics and Statistical Mechanics*, by W. Greiner,*et al.**A Modern Course in Statistical Physics*, by L.E. Reichl (Wiley, 1998)*Introductory Statistical Mechanics,*by R. Bowley and M. Sanchez*Thermodynamics and an Introduction to Thermostatistics,*by H.B. Callen*Fundamentals of Statistical and Thermal Physics,*by F. Reif*States of Matter,*by D.L. Goodstein

**Homework:** will be assigned at 1-2 week intervals and collected in class.
Assignments, due dates, and solutions will be posted at homework.
Homework is perhaps the most important component of the course and we strongly
urge you to complete it as close to the due date as possible; it will be difficult
to master the subject without keeping up with the homework. Late homework
must be submitted directly to the grader's campus mailbox and will be accepted,
with a penalty of 25%, until grading of the current assignment has been completed.
Collaboration on homework is permitted and use of *Mathematica* is encouraged.

** Mathematica: **a powerful symbolic manipulator which provides very
useful tools for the solving problems and exploring the results. Its symbolic
and graphical tools allow the student to focus more upon physics than upon algebra
and its numerical tools allow interesting problems which cannot be reduced to
simple closed forms to be investigated without developing customized computer
programs.

**Exams:** there will be two exams given during class periods (75
minutes) and a two-hour comprehensive final exam. The date and time of the
final exam will be announced when available. Make-up exams will be given only
when pre-arranged with the instructor or for unavoidable absences, such as
documented illnesses or emergencies.

**Grading:** graded work will be weighted 20% for each in-class exam
(40% total), 30% for homework, and 30% for the final exam. Letter grades are
based upon the distribution of numerical scores.

**Goals:** to acquire a sound understanding of the basic principles of
statistical mechanics and its application to realistic problems. Among the
skills we seek to develop are:

- isolate relevant aspects of a physical system
- produce appropriate model
- develop statistical description of system
- deduce major thermodynamic properties
- examine appropriate limiting behaviors (high and/or low temperature, classical limit, etc.)
- appreciate limits of model
- understand the behavior of important prototypical systems

**Review of thermodynamics**- Macroscopic description of equilibrium states
- Laws of thermodynamics
- Thermodynamic potentials and relationships
- Equilibrium and stability conditions
- Phase transitions

**Basic principles**- Density matrix formalism
- Statistical postulates
- Disorder and entropy
- Multiplicity functions
- Thermal interaction
- Temperature
- Statistical interpretation of thermodynamics

**Microcanonical ensemble**- Enumeration of microstates
- Large numbers
- Binary systems
- Noninteracting oscillators

**Canonical ensemble**- Definition and properties
- Thermodynamics
- Factorizable systems
- Paramagnetism
- Lattice vibrations
- Blackbody radiation

- Mean-field model of spontaneous magnetization
- Fluctuations and correlations

**Grand canonical ensemble**- Definition and properties
- Thermodynamics
- Occupation representation
- Classical
- Bose-Einstein
- Fermi-Dirac

**Semiclassical systems**- Classical phase space
- Entropy
- Maxwell-Boltzmann distribution
- Equipartition and virial theorems
- Diatomic molecules
- Virial expansion for fluids

**Bose systems**- Thermodynamics of ideal Bose systems
- Bose-Einstein condensation
- Superfluidity

**Fermi systems**- Thermodynamics of ideal Fermi systems
- Degenerate Fermi systems
- Electron gas
- Atomic nuclei
- White dwarf stars

- Superconductivity