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YESHIVA UNIVERSITY
YESHIVA COLLEGE
Semester:
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Fall 1999
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Course:
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1520 Advanced Statistical Physics
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Lecture hours:
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Monday 6:30-7:20
Wednesday: 6:30 – 7:45
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Practicum Hours:
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Monday : 7:20 – 9:10
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Instructor:
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Dr. Gabriel Cwilich
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Office:
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Belfer 1118 - Phone: 960 - 5342
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e-mail:
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Protosyllabus
Initial Text:
Thermal Physics
C. Kittel and H. Kroemer (K2)
(Second Edition, W.H. Freeman)
complemented by
Fundamentals of Statistical and Thermal Physics
F. Reif
(Mc Graw Hill)
We will start by a review (and expansion) of the basics of Statistical
Mechanics
 | Probability Distributions: Binomial, Random Walks, Gaussian. |
| Basic Postulates, Equilibrium and Statistical concepts of Thermodynamics. |
| Phase Space, Ensambles, Basic Methods (Partition Function and all that) |
| Classical ideal gas. |
| Chemical Potential and species equilibrium |
| Quantum statistics. |
Then we will consider in deep some applications of quantum and
classical statistical systems.
| Review of Photon gas and phonon gas |
| Bose-Einstein Condensation. |
| Superfluidity . Superconductivity |
| Fermi-Dirac statistics. Electrical Conductivity. |
| Semiconductors. |
| Theory of Phase transitions. Landau theories. The Ising Model |
| Modern approaches. Scaling and the Renormalization Group. |
| Non-equilibrium Stat. Mech. Boltzmann equation. Transport theory. |
Simultaneously we will choose a series of topics that will be explored
computationally, (some of them as a complement to the theoretical discussion, but in most
of them the emphasis will be on the numerical experimentation)
| Random generators and statistical distribution. |
| Random walks (straight, biased, self avoiding, and multiple walkers) |
| Spreading phenomena (clustering, forest fires) |
| Accretion Phenomena (Eden models, Diffusion limited aggregation and fractal dimensions) |
| Percolation |
| Ising systems |
| Connection to evolution models (punctuated equilibrium) |
| Cellular automata. Game of life. |
| Avalanches, sandpiles, earthquakes, and all that (Self organized criticallity). |
| Excitable Media (neuron activity, chemical excitations, epidemiology) |
| Traffic flow problems |
Here we might use texts as
- A Physicist’ Guide to Mathematica, by Patrick Tamm (Academic Press)
- Computer Simulations with Mathematica, by R. Gaylord and P. Wellin, (Telos)
- Modeling Nature, Cellular Automata Simulations with Mathematica, by R. Gaylord and K.
Nishidate, (Telos)
Another possible direction is including some specific topics of
computational techniques that are standard in Physics that are not discussed at all (or
just introduced ad-hoc) in other Physics courses.
| Interpolation methods (Lagrange, Splines, Least Squares) |
| Numerical Differentiation and Integration. |
| Zeros and extreme finding ( Bisection, Newton-Raphson) |
| Numerical solution of ordinary differential equations (Euler, Runge-Kutta) |
| Numerical Methods for Matrices (Diagonalizing, Eigenvalue problems, the Lanczos
Algorithm) |
| Spectral analysis (Fourier, Fast Fourier, Wavelets) |
| Methods for Partial Differential Equations. Boundary Problems. |
Possible sources here might be
A First Course in Computational Physics, by Paul DeVries, (J. Wiley)
An Introduction to Computational Physics, by Tao Pang (Cambridge)
Computational Physics, by Nicholas Giordano (Prentice Hall)
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