ECTS credits ECTS credits: 3
ECTS Hours Rules/Memories Student's work ECTS: 51 Hours of tutorials: 3 Expository Class: 9 Interactive Classroom: 12 Total: 75
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Particle Physics
Areas: Condensed Matter Physics, Theoretical Physics
Center Faculty of Physics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
The goal of this course is to introduce the student in the statistical mechanics characterization of strongly coupled systems, providing the essential bases of this discipline and showing him different applications of this. In the course some of the formalisms that allow the description of systems with strongly coupled degrees of freedom (mean field theory, renormalization group...), overcoming the treatment of ideal systems characteristic of the introductory degree courses in Physics, are presented. Special attention is paid to the role of the interaction potential and to the corresponding correlation functions. As for interacting quantum systems strongly coupled many-body systems will be analyzed both for the fermionic and the bosonic cases. Finally, new trends in Statistical Mechanics based on the generalization of the classical measure of information, the Boltzmann-Gibbs entropy, allowing the description of non extensivities in the thermodynamic magnitudes derived from multifractality in the phase space, long-range interactions, etc., will be presented.
LEARNING OUTCOMES
The learning results are both theoretical and practical in nature, since it is intended that students learn not only the theoretical bases of this subject, but also concrete applications to systems of diverse nature. In particular, it is expected that, once the subject has been completed, or gender students will be able to:
1. Analyze the concepts of statistical mechanics of equilibrium of interactive systems.
2. Apply the basic principles and concepts of discipline.
3. Ability to learn autonomously and have an entrepreneurial spirit.
4. Communicate your own points of view persuasively.
5. Contextualize the state of evolution of the current historical moment.
6. Manage the mean field formalism and understand its main applications.
7. Understand the fundamentals of the microscopic theory of quantum liquids, making special emphasis on superfluids and superconductivity.
8. Understand the main concepts of the renormalization group.
9. Handling of non-conventional statistical entropies (Renyi, Shannon...).
10. Manage bibliographic and documentary resources: databases, navigation, etc.
Introduction. Maximum entropy principle: Boltzmann-Gibbs entropy and statistical ensembles. Brief review of ideal systems: classic and quantum ideal gases.
Interacting systems. Classical systems. Distribution functions. Correlation functions. Mayer cluster expansion. Microthermodynamics: the energy equation of state, the virial equation of state and the compressibility equation. Integral equation theories: Ornstein-Zernike equation and closure relations .
Mean-field theories. Formal basis of mean-field theories: Bogoliubov’s inequality. Applications: van der Waals gas and the Debye-Hückel plasma theory. Thomas-Fermi theory. Bragg-Williams theory, Bethe lattice, and the theories of Flory-Huggins and of Schentjes-Fleer.
Order-disorder theory. Ising model. N-vectorial model: Potts, XY and Heisenberg models. Mean-field solution of the Ising model. Landau theory and Ginzburg criterion. Gaussian approximation. Correlation functions. Critical phenomena: Critical exponents and scaling.
Interacting Fermi and Bose systems. Applications. Quantum liquids: Fermi and Bose liquids. Plasmons and polarons.
Introduction to the renormalization group. Kadanoff transformations. Critical surface and fixed points. Scaling fields and fluxes of the renormalization group. Anomalous dimensions and beta function. Universality. Examples.
Non extensive thermodynamics and Statistical Mechanics. Generalization of the Boltzmann-Gibbs entropy for complex systems: non extensive Tsallis entropy. Other information measures: Renyi entropy.
Basic:
[1] L.M. Varela, H. Montes y T. Méndez, Mecánica Estadística, USC Editora, 2024
[2] Teacher's notes of the subject and collections of solved exercises, which will be available to students in the Virtual Campus of the USC.
Complementary:
[1] R. P. Feynman, Statistical Mechanics: a Set of Lectures. Reading: Addison-Wesley, 1990.
[2] M. Le Bellac. Quantum and Statistical Field Theory (vol. I). Oxford: Clarendon, 1991.
[3] M. Le Bellac, Equilibrium and non-Equilibrium Statistical Thermodynamics. Cambridge:Cambridge University Press, 2004.
[4] J. P. Hansen and I. R. McDonald, Theory of Simple Liquids New York: Academic Press, 1986.
[5] L. E. Reichl, A Modern Course in Statistical Physics 1 edición. Austin: University of Texas Press, 1991; 3 edición, Weinheim: Wiley-VCH Verlag GmbH, 2009.
[6] W. T. Grandy, Foundations of Statistical Mechanics. Dordrecht: D. Reidel, 1998.
[7] L. D. Landau and E.M. Lifshitz, Curso de Física Teórica, vol. 5 Física Estadística (Reverté, Barcelona, 1986-1988).
BASIC
CB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context
CB7 - Knowledge about how to apply the knowledge acquired and their ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of study
CB8 - Ability to integrate knowledge and face the complexity of making judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments
CB9 - Ability to communicate conclusions and the knowledge and ultimate reasons that sustain them to specialized and non-specialized audiences in a clear and unambiguous way
CB10 - Learning skills allowing to continue studying in a way that will be largely self-directed or autonomous.
GENERAL
CG01 - Acquire the ability to perform team research work.
CG02 - Be able to analyze and synthesize.
CG03 - Acquire the ability to write texts, articles or scientific reports according to publication standards.
CG04 - Become familiar with the different modalities used to disseminate results and disseminate knowledge in scientific meetings.
CG05 - Apply knowledge to solve complex problems.
TRANSVERSAL
CT01 - Ability to interpret texts, documentation, reports and academic articles in English, scientific language par excellence.
CT02 - Develop the capacity to make responsible decisions in complex and / or responsible situations.
SPECIFIC
CE05 - Acquire advanced training aimed at research and academic specialization, which will allow to acquire the necessary knowledge to gain access to the doctorate.
CE08 - Acquire an in-depth knowledge of the structure of matter in the low energy regime and its characterization ..
CE09 - Master the set of tools necessary to analyze the different states of matter.
CE13 - Master interdisciplinary tools, both theoretical and experimental or computational, to successfully develop any research or professional activity framed in any field of Physics.
CE14 - Be able to perform the essentials of a process or situation and establish a working model of it, as well as perform the required approximations in order to reduce the problem to a manageable level. Demonstrate critical thinking to build physical models.
The program will be developed through magisterial classes. The student will be given all the necessary material for the study of the subject, as well as for the realization of the work topics proposed by the professors in charge of it. The student will have the corresponding tutorial hours, which may be face-to-face or telematic.
A course will be activated on the Moodle platform of the Virtual Campus, to which information of interest to students will be uploaded, as well as various teaching materials.
The general methodological guidelines established in the memory of the USC Master in Physics will be followed. The classes will be face-to-face and the distribution of expository and interactive hours follows that specified in the memory of the master.
The tutorials can be face-to-face or online. If they are online they will require an appointment, which is also recommended in person.
The evaluation of the subject will be made up of a combination of: a) continuous evaluation throughout the course and b) a work topic to prepare throughout the course and present orally at the end of it.
Although the subject of work will be carried out following the guidelines of the professor in charge of the subject, the personal initiative taken by the student in preparing it will be highly valued.
Continuous assessment (class attendance, participation, ...) 20%
Presentation of works 80%
The student's grade in the second opportunity will correspond to the grade obtained in the corresponding official exam.
In cases of fraudulent completion of exercises or tests, the following will apply to the provisions of the "Regulations for evaluating students' academic performance and reviewing grades":
"Article 16. Fraudulent performance of exercises or tests.
The fraudulent performance of any exercise or test required in the evaluation of a subject will imply the qualification of failed in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. It is considered fraudulent, among other things, the realization of plagiarized works or obtained from sources accessible to the public without re-elaboration or reinterpretation and without citations to the authors and the sources ”.
The subject consists of 3 ECTS, therefore the total of work hours of the student, including activities of evaluation is of 75 hours, structured in:
- 20 hours of magisterial class.
- 10 hours of seminars and 1 of tuitions.
- 44 hours of personal work of the student.
1. The constant study, the daily follow-up and internalization of the theoretical classes and of seminars, will allow the student a good profit in the matter and the optimization of his time.
2. Consulting the recommended bibliography.
3. Using the individual tuitions and the seminars of the professors of the matter for the accomplishment of the assigned works.
Luis Miguel Varela Cabo
Coordinador/a- Department
- Particle Physics
- Area
- Condensed Matter Physics
- Phone
- 881813966
- luismiguel.varela [at] usc.es
- Category
- Professor: University Professor
Alfonso Vázquez Ramallo
- Department
- Particle Physics
- Area
- Theoretical Physics
- Phone
- 881813990
- alfonso.ramallo [at] usc.es
- Category
- Professor: University Professor
Hadrián Montes Campos
- Department
- Particle Physics
- Area
- Condensed Matter Physics
- hadrian.montes [at] usc.es
- Category
- Posdoutoral USC
| Monday | |||
|---|---|---|---|
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 7 |
| Tuesday | |||
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 7 |
| Wednesday | |||
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 7 |
| Thursday | |||
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 7 |
| Friday | |||
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 7 |
| 01.08.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 5 |
| 07.07.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 5 |