Syllabus - TAU



Syllabus (subject to changes)

Graduate Level Statistical Physics I

First semester 2008, School of Physics Tel Aviv University

Lecturer: Eshel Ben-Jacob Teaching assistance: Guy Ron

10+1 weeks: 3 hours frontal lectures and 1 hour Exercise lecture per week

Lectures:

Wednesday 17:00-19:00 Melamed lecture hall 06

Thursday 17:00-18:00 Melamed lecture hall 06

Tirgulim: Thursday 18:00-19:00 Melamed lecture hall 06

Relevant material can be found in Ben-Jacob home page

Ben-Jacob’s emails eshelbj@ 

Ron’s Emails ronguy@tauphy.tau.ac.il ronguy@muon.tau.ac.il

Topics that will not be covered in 2008 are marked

Chapter 1: Concise review of thermodynamics (2 weeks)

Extensive and intensive variables, Equilibrium and the Ergodic theorem, the Entropy and the Fundamental Equation, Euler’s relations, and the thermodynamic potentials (Free energies), Thermodynamic machines, Maxwell’s relations, Maxwell demon, Szilard’s and Brillion’s interpretations, Einstein’s interpretation of Planck equation and and photons, Schrodinger’s negative entropy criteria.

Tutorial will include: Complete differentials, partial derivatives relations, Legendre’s transformation, Black body radiation

Bibliography: Distributed notes, Ben-Jacob’s book (Hebrew), The Open University course, H.B. Callen, "Thermodynamics and an Introduction to Thermostatistics," 2d ed., Wiley (1985).

Chapter 2: The foundations of Statistical Physics (4 weeks)

The fundamental assumption: the micro-level – macro-level relations, the notion of the number of microscopic states, the notion of the ensembles, The connection with the thermodynamic potentials, The Micro-canonic and the Canonic ensembles, the chemical potential and the Grand-canonic ensemble, classical ideal gas and the Maxwell distribution, Ideal gas of fermions and the Fermi-Dirac distribution, Ideal gas of bosons and the Bose-Einstein distribution, Bose-Einstein condensation an super-fluidity, Super-conductivity, Cold atoms.

Tutorial will include: the heat capacity of electrons in solids, heat capacity of phonons, black body radiation revisited.

Bibliography: Distributed notes, R.K. Pathria, Statistical Mechanics, 2nd Edition, and `Statistical Mechanics' by S.K. Ma (World Scientific 1985)

Chapter 3: Phase transitions and critical phenomena (3 weeks)

First and second order phase transitions, Ising model, Mean Field Theory and landau Theory, Coarse graining and Scaling, Critical exponent, Universality, Renormalization Group, Correlations, finite-size scaling, Spin-glass and Frustration.

Tutorial will include: Ising in two dimensions, Potss model, the X-Y model, Spin-glass, Metropolis and Monte-Carlo simulations,

Bibliography: N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, Reading, 1992) and P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995)

Chapter 4: Time dependent phenomena (Stochastic processes) (2 weeks)

Fluctuations and noise (white noise, colored noise and shot noise), Random walk, the Langevin equation, Einstein’s Fluctuation-dissipation relations, the Diffusion equation, the Fokker-Planck equation, Kramers activation theory.

Tutorial will include: Levy walk and Levy distribution, 1/f noise and fractals, Phase-space and the Liouville equation, the Master equation, solutions of the Fokker-Planck equation for special cases.

Bibliography: Distributed notes, N. G. Van Kampen Stochastic Processes in Physics and Chemistry and H. Risken The Fokker-Planck Equation: Methods of Solutions and Applications, and also can be interesting to look at `Theory of the Brownian Movement' by A. Einstein

Chapter 5: Advanced topics (2 weeks) -

Thermodynamics of Black Holes (Bekenstein entropy and Hawking radiation), Polymers entropy, membranes fluctuations, Protein folding, the properties of water, self-organization and pattern formation, information theory.

Bibliography: `Equilibrium Statistical Physics', 2nd edition, by M. Plischke and B. Bergersen, and we will distribute a list of links like the one below.

Information in the Holographic Universe

|Information in the Holographic Universe; August 2003; Scientific American Magazine; by Jacob D. Bekenstein; 8 Page(s). Ask |

|anybody what the physical world ... |

|index.cfm?fa=Products.ViewIssuePreview&ARTICLEID_CHAR=4D0EEDAF-DEB7-FC61-90CF673... - 15k - Cached - |

|Similar pages |

Additional References and links

`Statistical Mechanics', by L.D. Landau and E.M. Lifshitz (Pergamon) - a really good book, with many of the classical topics that we will discuss beautifully presented.  E ven the old edition (one volume) is good.  Newer edition is split into two volumes; the second volume is not needed for this course.

`Thermal Physics', Second Edition, by C. Kittel and H. Kroemer (Freeman and Co, New York 1984). Kittel wrote the first edition of this, in 1969, and Kroemer co-authored the second edition, in 1980. (This is the same Herbert Kroemer that won the Nobel Prize in 2000.) This has been a very widely used book for the last twenty years. It deals almost exclusively with statistical mechanics, with one chapter that derives the laws of thermodynamics. The methods used to derive the statistical distribution laws were very novel when the first edition was published, quite different from the counting techniques used in the earlier books. For me, this is still slightly controversial. The problems at the ends of chapters are excellent.

D. Chandler, "Introduction to Modern Statistical Mechanics" Oxford University Press (1987).

Leo P. Kadanoff, Statistical Physics: Statics, Dynamics and Renormalization (World Scientific, Singapore, 2000)

Lecture Notes in Statistical Mechanics

|The Renormalization-Group Methods; Momentum-Space Renormalization Group. Appendices. Further Reading; Distribution |

|Functions; Maxwell Relations ... |

|www-f1.ijs.si/~vilfan/SM/cont.html - 2k - Cached - Similar pages |

More advanced oldies

Kittel and Kroemer "Thermal Physics". Kittel wrote the first edition of this, in 1969, and Kroemer co-authored the second edition, in 1980. (This is the same Herbert Kroemer that won the Nobel Prize in 2000.) This has been a very widely used book for the last twenty years, although last year the book store told me it was out of print. It deals almost exclusively with statistical mechanics, with one chapter that derives the laws of thermodynamics. The methods used to derive the statistical distribution laws were very novel when the first edition was published, quite different from the counting techniques used in the earlier books. For me, this is still slightly controversial. The problems at the ends of chapters are excellent.

Stowe "Statistical Mechanics and Thermodynamics". I am less familiar with this than any of the other books listed. It appeared in 1984. In some ways it follows the conventional format, treating Classical Thermodynamics and then Statistical Mechanics, but, before any of this there is a discussion of small systems and ideas from statistics, and the treatment of thermodynamics makes use of these ideas rather than taking a purely macroscopic approach. One reason for looking at it is that Dan Schroeder (see below) credits it as one of his inspirations.

The New Wave

For some reason, there was a dearth of new books on thermal physics in the 1980's and 1990's. Perhaps we all assumed that the last word had been written. For many years, I used Zemansky for the first semester and Kittel and Kroemer for the second. Then there was a flurry of new books. Three appeared in 1999, and 2000, and more are rumored. One characteristic of the new books is that they are tailored to a one semester course on thermal physics, but all the authors try to do justice to both sets of ideas.

Schroeder "Thermal Physics". Written in a very chatty style, that I wish I had thought of. There is an immense number of problems, embedded in the text rather than left to the chapter ends. The way to use this book seems clearly to work a lot of problems as you go. Schroeder says that there is too much material for one semester, but that it is still primarily intended for a one semester course. The presentation starts with microscopic ideas, and freely mixes up microscopic and macroscopic concepts all the way through

Baierlein "Thermal Physics" (there seem to be more new books than new titles). This has much in common with Schroeder. It uses microscopic ideas to motivate and justify the second law. But its treatment both of thermodynamics and statistical mechanics is more formal that Schroeder's. (e.g. there is a chapter called "The Canonical Probability Distribution". Schroeder buries the word "canonical" in a footnote.) However, the treatment of Classical Thermodynamics does not follow the traditional approach through heat engines, and the treatment of the probability distributions follows Kittel and Kroemer's methods rather than, for example, Reif's or Crawford's.

Carter "Classical and Statistical Thermodynamics". This is by far the most traditional of the new books. It follows the pattern of Crawford and of Morse, developing Classical Thermodynamics using a macroscopic approach, and then Statistical Mechanics using the traditional Lagrange multiplier techniques. However, Carter says that you can cover all of this in one semester.

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