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B013261 - STATISTICAL MECHANICS I
Main information
Course Content
Suggested readings
Learning Objectives
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2009-10
Coorte 2009 - Second Cycle Degree in SCIENZE FISICHE E ASTROFISICHE
Course year
First year -
Belonging Department
Physics and Astronomy
Course Type
Single education field course
Scientific Area
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS
Credits
6
Teaching Hours
50
Teaching Term
⇒
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Course Content
Theory of statistical ensembles: density operators, postulates of statistical mechanics, quantum statistical ensembles, classical limit. Theory of transformations between statistical ensembles. Phase transitions and critical phenomena: singularities in thermodynamic functions, Lee-Yang theory. Spontaneous symmetry breaking and ergodicity breaking. Mean field theory and Landau-Ginzburg theory. Universality, scale invariance, critical exponents. Renormalization group.
Suggested readings (Search our library's catalogue)
•R. Balian, "From microphysics to macrophysics" (Springer), in particolare il Vol. I.
•L. Peliti, "Appunti di meccanica statistica" (Bollati Boringhieri).
R. P. Feynman, "Statistical mechanics" (Perseus).
•J. J. Binney et al., "The theory of critical phenomena" (Oxford).
•N. Goldenfeld, "Lectures on phase transitions and the renormalisation group" (Addison-Wesley).
•J. Cardy, "Scaling and renormalization in statistical physics" (Cambridge).
•L. Peliti, "Appunti di meccanica statistica" (Bollati Boringhieri).
R. P. Feynman, "Statistical mechanics" (Perseus).
•J. J. Binney et al., "The theory of critical phenomena" (Oxford).
•N. Goldenfeld, "Lectures on phase transitions and the renormalisation group" (Addison-Wesley).
•J. Cardy, "Scaling and renormalization in statistical physics" (Cambridge).
Learning Objectives
Knowledge acquired:
The course is composed of two parts. In the first part there is an exposition of the fundamental concepts of equilibrium statistical mechanics and also quite advanced topics are discussed, e.g. the theory of transformations between statistical ensembles. This part of the course is thought like a fulfillment of the course of Statistical Mechanics usually followed during the first level degree. In any case it is usable also by those students who don’t have a preexisting preparation in Statistical Mechanics.
The second part of the course is completely devoted to phase transitions: after a phenomenological introduction, conceptual nodes are dealt with (thermodynamic singularities, breaking of symmetries and of ergodicity) followed by the theory of critical phenomena (mean field, Landau theory and Landau-Ginzburg theory, scale invariance and renormalization group).
Competence acquired: Mastering of conceptual bases of equilibrium statistical mechanics and of phase transitions theory. Solution of simple but nontrivial model in statistical mechanics.
Skills acquired (at the end of the course): Tools to understand more advanced monographs on statistical mechanics and phase transitions as well as of part of research literature.
The course is composed of two parts. In the first part there is an exposition of the fundamental concepts of equilibrium statistical mechanics and also quite advanced topics are discussed, e.g. the theory of transformations between statistical ensembles. This part of the course is thought like a fulfillment of the course of Statistical Mechanics usually followed during the first level degree. In any case it is usable also by those students who don’t have a preexisting preparation in Statistical Mechanics.
The second part of the course is completely devoted to phase transitions: after a phenomenological introduction, conceptual nodes are dealt with (thermodynamic singularities, breaking of symmetries and of ergodicity) followed by the theory of critical phenomena (mean field, Landau theory and Landau-Ginzburg theory, scale invariance and renormalization group).
Competence acquired: Mastering of conceptual bases of equilibrium statistical mechanics and of phase transitions theory. Solution of simple but nontrivial model in statistical mechanics.
Skills acquired (at the end of the course): Tools to understand more advanced monographs on statistical mechanics and phase transitions as well as of part of research literature.
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...):
150
Hours reserved to private study and other individual formative activities:
100
Contact hours for: Lectures (hours): 50
150
Hours reserved to private study and other individual formative activities:
100
Contact hours for: Lectures (hours): 50
Further information
Office hours:
Teacher: Dott. L. Casetti
Location: Physics Department, Room 304 (II floor) tel. 0554572311 (int. 2311)
e-mail: lapo.casetti@unifi.it, casetti@fi.infn.it
Wednesday 16:30 – 19:30; or contact the teacher for other possibilities
Teacher: Dott. L. Casetti
Location: Physics Department, Room 304 (II floor) tel. 0554572311 (int. 2311)
e-mail: lapo.casetti@unifi.it, casetti@fi.infn.it
Wednesday 16:30 – 19:30; or contact the teacher for other possibilities
Type of Assessment
The final test is a traditional oral test. Nevertheless students who would like to may prepare a presentation of a subject, chosen together with the teacher, which contains an in-depth examination of one or more particular aspects of the course under a more general point of view. In this case, the first half of the exam will be the presentation and the discussion of the chosen subject, the second half will be a traditional oral test covering other aspects of the course.
Course program
Theory of statistical ensembles: density operators, postulates of statistical mechanics, quantum statistical ensembles, classical limit. Theory of transformations between statistical ensembles. Phase transitions and critical phenomena: singularities in thermodynamic functions, Lee-Yang theory. Spontaneous symmetry breaking and ergodicity breaking. Mean field theory and Landau-Ginzburg theory. Universality, scale invariance, critical exponents. Renormalization group.