PHYS 252

Statistical Mechanics II

Course Description

PHYS 252 is the second course in a series of graduate courses in Statistical Mechanics for MS Physics students. It starts out with discussions on canonical ensemble theory to treat systems that are in contact with a heat bath. The partition function is introduced and used to calculate thermodynamic quantities such as the mean energy, entropy, heat capacity, magnetization, and susceptibility of the system. Discussions are then extended to the grand canonical ensemble theory to include systems that are in contact with a particle and energy reservoir. This paves the way for discussions on quantum statistics and systems of indistinguishable particles. The course ends with the introduction and use of the density matrix to calculate the thermodynamic quantities of a quantum system of free particles.

Course Learning Outcomes

After completing this course, you should be able to:

• differentiate between microcanonical, canonical, and grand canonical ensembles;

• determine the thermodynamic properties and behavior of classical systems using either microcanonical, canonical, or grand canonical ensembles; and

• deduce the thermodynamic properties of quantum systems based on quantum statistics.

Course Outline

  1. The Canonical Ensemble

    • System in equilibrium with a heat bath

    • A system in the Canonical Ensemble

    • Physical significance of the statistical quantities in the Canonical Ensemble

    • Partition Function

    • Classical systems

    • Energy fluctuations

    • Equipartition of Energy Theorem

    • Virial Theorem

    • A system of harmonic oscillators

    • Statistics of paramagnetism

    • Negative temperatures

  2. The Grand Canonical Ensemble

    • System in equilibrium with a particle-energy reservoir

    • A system in the Grand Canonical Ensemble

    • Physical significance of the statistical quantities in the Grand Canonical Ensemble

    • Density and energy fluctuations

    • Phase diagrams

    • Clausius-Clapeyron Equation

  3. Quantum Statistics

    • Quantum-mechanical Ensemble Theory

    • Density matrix

    • System of indistinguishable particles

    • System of free particles

Mode of Delivery

The course will follow the schedule stated in this Syllabus. All course materials, i.e., this Syllabus, the Lecture Activities, lecture slides, and supplementary materials, are going to be available in the Canvas Learning Management System (LMS) for the course. Online lectures are going to be held twice a week via Zoom meetings.

References

The main reference for this course is:

• R.K. Pathria and P.D. Beale, Statistical Mechanics, 3rd Edition, Elsevier, 2011.

Supplementary references are:

• J.D. Walecka, Introduction to Statistical Mechanics, World Scientific, 2011.

• F. Schwabl and W.D. Brewer, Statistical Mechanics, 2nd Edition, Springer, 2006.

• R. Reif, Fundamentals of Statistical and Thermal Physics, Waveland Press, 2008.

Lecture Slides

• Lecture Slides 1 • Lecture Slides 11

• Lecture Slides 2 • Lecture Slides 12

• Lecture Slides 3 • Lecture Slides 13

• Lecture Slides 4 • Lecture Slides 14

• Lecture Slides 5

• Lecture Slides 6

• Lecture Slides 7

• Lecture Slides 8

• Lecture Slides 9

• Lecture Slides 10

About the Instructor

Name: Eduardo C. Cuansing Jr., Ph.D.

Email Address: eccuansing at up.edu.ph

Homepage: https://sites.google.com/up.edu.ph/eduardo-c-cuansing/home

Eduardo C. Cuansing Jr., Ph.D., is a Professor at the Institute of Mathematical Sciences and Physics (IMSP). He earned his B.S. Physics from the University of the Philippines Diliman and his Ph.D. Physics from Purdue University. He was a postdoctoral researcher at the University of Pittsburgh and the National University of Singapore. He was also previously a faculty member at the University of the Philippines Diliman, De La Salle University, and the Ateneo de Manila University. He currently heads the Quantum Transport and Quantum Thermodynamics (QT2) research group. His research is in theoretical and computational physics, in specific areas such as quantum transport, nonequilibrium physics, quantum thermodynamics, and phase transitions and critical phenomena. He was previously the President of the Samahang Pisika ng Pilipinas (Physics Society of the Philippines). He is currently the Vice Chair of Division IX (Physics) at the National Research Council of the Philippines (NRCP) and a member of the General Council of the Asia Pacific Center for Theoretical Physics (APCTP).