## Spring 2011

**Lecturer:**** Eduardo Mucciolo** (office in PSB 457, ext 3-1882, e-address: mylastname at physics dot ucf dot edu

**Schedule and Location:** Lectures on Tuesdays and Thursdays, 1:30-2:45 pm, in the Math and Physics Building, room 306. Office hours: Tuesdays and Thursdays 3:00 – 4:00 pm. Contact the instructor (by phone or email) if you need help outside the office hour slots.

**Credit hours:** 3 units.

**Prerequisites: **Thermal and Statistical Physics at the undergraduate level (PHY 3503) and elementary probability and statistics theory (at the level of STA 3032). Quantum Mechanics at the undergraduate level (PHY 4604) is highly recommended.

**Content:**

1)

*Review of Thermodynamics*: basic concepts and definitions; zeroth and first laws; Carnot cycle; entropy; second law; thermodynamic potentials; Maxwell relations; third law.

2) *Some Fundamentals of Statistics*: basic definitions; binomial distribution; Poisson distribution; Gaussian distribution; characteristic function; central limit theorem; random walk.

3) *Classical Statistical Mechanics*: many-particle systems in equilibrium; microcanonical ensemble; Liouville’s theorem; equal a priori probability postulate; entropy; connection with thermodynamics; ideal gas applications; Gibbs paradox; two-level systems.

4) *Canonical and Grand Canonical Ensembles*: system+reservoir in equilibrium; partition function; thermodynamics; solid-vapor equilibrium; classical non-ideal gas; generalized equipartition theorem.

5) *Quantum Statistical Mechanics*: indistinguishable particles; density matrix; ensemble averages; Fermi-Dirac and Bose-Einstein statistics; equation of state for ideal gases; thermal length.

6) *Fermi Gas*: state equation and other thermodynamic properties; Fermi sea, surface, and energy; Sommerfeld integrals; nondegenerate and degenerate limits; specific heat; Pauli paramagnetism; Landau diamagnetism; electrons in metals.; white dwarf stars.

7) *Bose Gas*: state equation and other thermodynamic properties; divergences in the thermodynamic limit; high and low temperature limits; Bose-Einstein condensation; black-body radiation; vibrations in crystalline solids.

8) *Phase Transitions and Critical Phenomena*: van der Waals equation; ferromagnets; Landau theory; scaling.

9) *Non-Equilibrium Statistical Mechanics*: Boltzmann equation; Langevin equation; Fokker-Planck equation; master equation.

**Textbook:***Introduction to Statistical Physics*, by Silvio R. A. Salinas (Springer-Verlag, New York, 2001); ISBN 0-387-95119-9 (hard cover). The material covered in this course is very standard and can be found in many other textbooks. They differ mainly on the order of topics, length, and notation. Therefore, students are encouraged to check other books and find the most suitable for their studies. Suggested titles are: *Statistical Mechanics*, 2nd ed., K. Huang (John Wiley and Sons, 1987); *Statistical Mechanics*, 2nd ed., R. K. Pathria (Butterworth-Heinemann, 1996); *Statistical Physics*, 3rd ed., E. M. Lifshitz and L. D. Landau (Butterworth-Heinemann, 1999).

**Grading:** The overall grade will be based on the homework average (40%), a mid-term exam (20% each), and a final exam (40%). Problem sets will be handed out every two weeks or so and graded with the same rigor as an exam. Grading will be done over a scale from 0 to 100, with letter grades distributed as: A (100-96), A- (95-91), B+ (90-86), B (85-81), B- (80-76), C+ (75-71), C (70-66), C- (65-61), D+ (60-56), D (55-51), D- (50-46), and F (45-0). Late homework will receive no points but will be counted toward the average. Students are encouraged to interact outside class and discuss homework assignments, but solutions must be developed individually.

The tentative day for the mid-term exam is February 23 (Thursday) during normal lecture time. The final exam has been scheduled for April 26 (Tuesday), from 1:00 pm to 3:50 pm in MAP 306.

*CALENDAR*

*READING ASSIGNMENTS AND OTHER MATERIALS*

PROBLEM SETS (pdf files)

#1 (due Friday, January 21)

#2 (due Friday, February 04)

#3 (due Friday, February 18)

#4 (due Friday, March 04)

#5 (due Friday, March 25 )

#6 (due Friday, April 08)

#7 (due Friday, April 22)

Eduardo Mucciolo 2011-03-01