Professor M. Tuckerman Office: 1001L Main Phone: 998-8471 E-mail: mark.tuckerman@nyu.edu
Books
The course will generally follow the book, Thermodynamics and Statistical
Mechanics by Greiner, Neise and Stöcker. However, there will be many
departures from the book and additional material not covered in the
book. For this reason, the following books are listed
as recommended references:
D.A. McQuarrie, Statistical Thermodynamics
K. Huang, Statistical Mechanics, 2 edition
R.P. Feynman, Statistical Mechanics, A set of lectures
Occasionally, material will be drawn from current literature in
statistical mechanics.
Course Outline
I.
Classical statistical mechanics:
A.
Clasical mechanics, equations of motion, Lagrangian
and Hamiltonian formulations.
B.
Phase space, phase space distribution functions,
Liouville's theorem for Hamiltonian and non-Hamiltonian systems.
C.
Equilibrium ensembles and thermodynamics:
1.
Microcanonical.
2.
Canonical.
3.
Isothermal-isobaric.
4.
Grand canonical.
D.
Applications:
1.
Ideal gas.
2.
Real gases and liquids:
a.
Structure and distribution functions.
b.
Virial equation of state.
c.
Perturbation theory.
d.
Reaction coordinates and free energy functions.
II.
Quantum statistical mechanics:
A.
Hilbert space, density matrix, quantum Liouville theorem.
B.
Quantum equilibrium ensembles.
C.
The Feynman path integral formulation.
D.
Applications:
1.
Quantum ideal gases:
a.
Boltzmann.
b.
Fermi-Dirac.
c.
Bose-Einstein.
2.
Proton transfer (an application of the path integral).
III.
Time-dependent processes:
A.
Time correlation functions:
1.
Linear response theory, Green-Kubo, and transport.
2.
Relation to spectra.
B.
Systems coupled to a bath:
1.
Generalized Langevin dynamics.
2.
The influence functional.
3.
Application to vibrational dephasing and energy relaxation.
IV.
Critical Phenomena:
A.
The Ising model:
1.
Exact solution in 1 dimension.
2.
Exact (Onsager) solution in 2 dimensions.
B.
Mean field theory.
C.
Scaling theory and renormalization.
Grading basis
Homework:............20%
Midterm:...............40%
Final:....................40%
Web resources
Notes for all lectures can be found on the course web page:
This semester, we will also make use of the new NYU online Blackboard service. This
Web site contains a variety of useful tools, including a discussion board,
a chat room, external links, and personalized pages for each student enrolled in the course.
The blackboard site can be accessed through your Home page at:
and clicking on the ``Academics'' tab. You will see the link for this course to
the blackboard site. If you do not have such an account, you should be able
to create one for yourself at
I encourage you to make use of the blackboard utilities. I will often post
announcements there and will check the discussion forum as often as I can.
I will also log onto the chat room as often as I can in case there are questions.
edition