A.A. 2018-2019


2º semestre



Statistical Physics 2





Lectures: Tuesday 11-13 Lecture Room V3p; Friday 11-13 Lecture Room V3p


Updated (unfortunately incomplete) iPad notes pdf


Structure of the course: there will be a set of “common” lectures on the theory of critical phenomena and real space renormalization group. Besides that, each student will work on a final project on a different subject, to be selected together with me: I will provide appropriate references for such “advanced issues”.


Reference books: K. Huang, Statistical Mechanics (KH); L.D. Landau and E.M. Lifshitz, Statistical Physics, Part 1 (LL); L.P. Kadanoff, Statistical Physics. Statics, Dynamics and Renormalization (LK), D. Sornette, Critical Phenomena in Natural Sciences (DS), L.E. Reichl,

A Modern Course in Statistical Physics (LR), D.P. Landau and K. Binder, A Guide to Monte

Carlo Simulations in Statistical Physics (LB), G. Mussardo, Il modello di Ising (GM), G.A. Baker, Jr., Quantitative theory of critical phenomena (GB), H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (NO), R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Ba), M.E.J. Newman and G.T. Barkema, Monte Carlo Methods in Statistical Physics (NB)


List of (old) available lessons (streaming on demand)  link  (starting march, 10;

former lectures refer to Statistical Physics 1)


Syllabus (common part) - Canard du jour


26-2-2019 - Introduction.

15-3-2019 - Ising models. 1d solution: free energy and correlations.

19-3-2019 - Peierls’ argument. Bragg Williams approximation.

22-3-2019 - Bethe Peierls approximation.

26-3-2019 - Kramers Wannier duality.

29-3-2019 - Exact solution of 2d Ising model.

02-4-2019 - Fluctuation dissipation theorem.

05-4-2019 - Mean field estimate of ν and η.

11-4-2019 - Widom scaling and scaling relations.

12-4-2019 - The gaussian model.

16-4-2019 - The spherical model.

30-4-2019 - Introduction to renormalization group.

03-5-2019 - Examples: 1d Ising, 2d Ising via high temperature expansion.

10-5-2019 - Relevant eigenvalues and scaling of the free energy.

14-5-2019 - Renormalization for 2d Ising on a triangular lattice.

21-5-2019 - Hierarchical models: renormalization of the Potts model on a diamond.










1º semestre



Meccanica analitica



Testi di riferimento: Landau: Meccanica (La); Lowenstein: Essentials of hamiltonian dynamics (Lo); Arnold: Mathematical methods of classical mechanics (Ar); Sommerfeld: Mechanics (So); Corben: Classical mechanics (Co), Lanczos: The variational principles of mechanics (Lz)


Collezione di problemi risolti: Lim Yung-kuo (ed.): Problems and solutions on mechanics


Note iPad aggiornate pdf


Sunto delle lezioni:


25-09-2018 -- Presentazione del corso. Alcuni richiami di meccanica elementare.

26-09-2018 -- Vincoli. Dal principio dei lavori virtuali alle equazioni di Lagrange.

02-10-2018 -- Esempi elementari di Lagrangiane. Coordinate cicliche. Struttura

                      generale dell’energia cinetica.

03-10-2018 -- Invarianza per trasformazione di coordinate. Teorema di Noether

                      lagrangiano.

09-10-2018 -- Principi variazionali. Equazioni di Eulero Lagrange.

10-10-2018 -- Geodetiche sulla sfera. Equazioni di Eulero Lagrange in presenza

                      di vincoli semiolonomi.

11-10-2018 -- Esercitazioni

16-10-2018 -- Forze centrali: il problema di Keplero.

17-10-2018 -- Scattering di Rutherford

23-10-2018 -- Moto traslazionale di un corpo rigido. Corpo rigido con un punto

                      fisso, angoli di Eulero.

24-10-2018 -- Tensore d’inerzia. Terne principali.

25-10-2018 -- Esercitazioni

30-10-2018 -- Equazioni di Eulero. Giroscopi: moto libero e in presenza di gravità.

31-10-2018 -- Trottola dormiente. Piccole oscillazioni attorno ad un equilibrio

                      stabile.

06-11-2018 -- Modi normali di una molecola di CO2

07-11-2018 -- Equazioni di Hamilton. Esempi di hamiltoniane.

08-11-2018 -- Esercitazioni.

13-11-2018 -- Equazioni di Hamilton e principi variazionali.

14-11-2018 -- Trasformazioni canoniche: funzioni generatrici.

20-11-2018 -- Trasformazioni canoniche: parentesi di Poisson.

21-11-2018 -- Trasformazioni canoniche infinitesime.

22-11-2018 -- Esercitazioni

27-11-2018 -- Punti di Lagrange

04-12-2018 -- Stabilità di L4

05-12-2018 -- Introduzione a sistemi integrabili e equazione di Hamilton-Jacobi

11-12-2018 -- Integrale completo dell’equazione di Hamilton-Jacobi.

12-12-2018 -- Simulazione di prova d’esame.

18-12-2018 -- Sistemi separabili: il caso del doppio centro in coordinate ellittiche.

19-12-2018 -- Applicazioni geometriche di principi variazionali.

20-12-2018 -- Esercitazioni


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Materiale supplementare (A.A. 2017-2018)


Note iPad complete  pdf


Le registrazioni delle lezioni sono disponibili al seguente link








Statistical Physics 1



Prerequisites: Classical and Quantum Mechanics. Elementary notions of Thermodynamics and Probability Theory.


Suggested reference books: K. Huang, Statistical Mechanics (KH); M. Kardar, Statistical Physics of Particles (MK); L.D. Landau and E.M. Lifshitz, Statistical Physics, Part 1 (LL); L.E. Reichl, A Modern Course in Statistical Physics (LR).


Supplementary reading: A. Sommerfeld, Thermodynamics and Statistical Mechanics (AS); A.I. Khinchin, Mathematical Foundations of Statistical Mechanics (Kh); C.J. Thompson, Classical Equilibrium Statistical Mechanics (CT); J.M. Yeomans, Statistical Mechanics of Phase Transitions (JY); M. Plischke and B. Bergersen, Equilibrium Statistical Physics (PB), J.P. Sethna, Entropy,

Order Parameters and Complexity (JS) web book, P.M. Chaikin and T.C. Lubensky, Principles

of Condensed Matter Physics (CL), R. Balian, From Microphysics to Macrophysics, Vol. 1 (RB),

G.H. Wannier, Statistical Physics (GW), F. Reif, Fundamentals of Statistical and Thermal Physics

(FR), E.A Guggenheim, Thermodynamics (EG) [to be continued ..]


Updated iPad screens pdf


Lectures available for streaming on demand  link (the course consists of lectures 1 to 15)


Syllabus:


10-10-2018 -- Introduction to the course.

23-10-2018 -- Thermodynamic description. First and second principle. (no pdf notes)

24-10-2018 -- Stability of equilibrium states. Thermodynamic potentials.

30-10-2018 -- Third law. Clausius Clapeyron equation.

31-10-2018 -- Van der Waals equation of state.

06-11-2018 -- Landau theories. (no pdf notes)

07-11-2018 -- Foundations of statistical mechanics

13-11-2018 -- The microcanonical ensemble

14-11-2018 -- The canonical ensemble. Tonks-Van der Waals gas.

20-11-2018 -- The grand canonical ensemble.

21-11-2018 -- The thermodynamic limit (Van Hove gas)

27-11-2018 -- The thermodynamic limit (lattice models). Cluster expansion.

04-12-2018 -- The second virial coefficient.

11-12-2018 -- Quantum statistical mechanics.

12-12-2018 -- Grand canonical partition function for bosons.

14-12-2018 -- Grand canonical partition function for fermions.

18-12-2018 -- The classical limit of the quantum partition function.

19-12-2018 -- Bose statistics: phonons.

08-01-2019 -- Debye theory.

09-01-2019 -- Bose Einstein condensation.

15-01-2019 -- Degenerate Fermi gas.

16-01-2019 -- Pauli paramagnetism. Landau diamagnetism.