
Statistical Physics
Code: 100174Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Physics | OP | 4 |
Contact lecturer
- Name :
- Juan Camacho Castro
- Email :
- juan.camacho@uab.cat
Teaching staff
- Javier Cristin Redondo
Group languages
You can consult this information at the end of the document.
Prerequisites
There are no official prerequisites. However, it is assumed that students have knowledge in Thermodynamics and notions of Statistical Mechanics, especially the concepts and methods of ensemble theory, and basic knowledge of quantum mechanics and electromagnetism.
Objectives
• Specific objectives:
2) To know the basic theory of stochastic processes and be able to apply it to simple cases
3) Understanding the elementary kinetic theory of transport processes and be able to apply it to dilute gases and quantum gases
4) To know simulation methods for the analysis of complex systems: Monte Carlo (Metropolis), Brownian dynamics, Langevin dynamics
Learning outcomes
- Communicate complex information in an effective, clear and concise manner, either orally, in writing or through ICTs, in front of both specialist and general publics.
- Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
- Work independently, take initiative itself, be able to organize to achieve results and to plan and execute a project.
- Working in groups, assume shared responsibilities and interact professionally and constructively with others, showing absolute respect for their rights.
- Describe the most important statistical groups and the assumptions underlying the theory of groups.
- Correctly apply the theory of ideal systems for groups of distinguishable and indistinguishable particles.
- Apply statistical physics to interacting particle systems.
- Deduce classical and quantum statistics and apply them correctly to different systems.
- Applying the tools of kinetic theory to describe transport processes.
- Describe the concept of stochastic process and apply their basic techniques to the description of physical systems.
- Apply the concept of frozen and wake degrees of freedom to predicting the heat capacity of gases.
- Quantify the contribution of each internal degree of freedom in the heat capacity of a gas in diatomic molecules.
- Qualitatively and quantitatively predict the macroscopic behaviour of ideal magnetic systems for classical and quantum moments.
- Reason the temperature dependence of heat capacity for electrons and the crystalline network.
- Apply Fermi statistics to a degenerate gas of relativistic particles.
- Describe and quantify Brownian motion.
- Describe the thermal denaturation of DNA and quantify it for certain simple models.
- Describe ion transport in passive and active membranes, quantifying it for certain simple models.
- Determine the fraction of molecules adsorbed on a macromolecule in simple models.
- Analyse stochastic processes and use them to model physical systems and in other ambits.
- Determine the magnetic response of a superparamagnetic nanoparticle and the behaviour in a dispersion of these particles.
- Analyse interacting particle systems through simple models and simulation techniques.
- Describe and Analyse the Bose-Einstein condensation.
- Describe the basis of Brownian motors.
- Apply the kinetic theory of quantum gases and predict the thermal conductivity of metals and insulators.
- Describe biological systems using techniques of statistical physics.
- Qualitatively and quantitatively describe the behaviour of system close to critical points and the concept of universality.
- Analyse biological systems using techniques of statistical physics.
- Distinguish between mean-field models and those that are not.
- Use mean-field approaches to describe physical systems.
- Define characteristic magnitudes to discern the relevance of different mechanisms.
- Describe and analyse the models of Weiss, Landau and Ising for magnetic systems with interaction.
- Apply different techniques of simulation for the study of systems with interaction to simple cases: Monte Carlo, molecular dynamics, Brownian dynamics and Langevin dynamics.
- Analyse random paths and use them to model real systems.
- Analyse simple stochastic equations.
- Identify situations in which a change or improvement is needed.
- Identify the social, economic and environmental implications of academic and professional activities within one's own area of knowledge.
Contents
1. Stochastic processes
1.1. Introduction. Brownian Motion
1.2. Random Walks
1.3. Langevin equation
1.4. Fokker-Planck equation
1.5. Brownian motors
2. Summary of statistical mechanics
2.1 Ensemble theory. Postulates
2.2 Microcanonical ensemble
2.3 Canonical ensemble.
2.4 Continuos and discrete energy spectra.
2.5 Classical and quantum limits. Thermal wavelength
2.6 Maxwell-Boltzmann statistics
2.7 Theorem of equipartition of energy
3. Ideal gas of diatomic molecules
3.1 The problem of heat capacity in gases
3.2 Internal degrees of freedom
3.3 Contribution of each degree of freedom to heat capacity
3.4 Poliatomic molecules
4. Magnetic systems
4.1 Spin ½ systems
4.2 Quantum paramagnetism
4.3 Classical paramagnetism
4.4 Superparamagnetism
5. Biological systems
5.1 Saturation curve of myoglobin. Langmuir isotherm
5.2 DNA denaturation
6. Interacting systems
6.1 Solid, liquids, gases.
6.2 Magnetic systems. Ferro-paramagnetic transition
6.3 Weiss model
6.4 Landau model
6.5 Ising model
6.6 Critical points. Universality
6.7 Monte Carlo methods. Metropolis algorithm
7. Ideal quantum gas
7.1 Distinguishable and indistinguishable particles
7.2 Microstates in quantum statistical mechanics
7.3 Calculation of grand canonic partition functions in an ideal gas
7.4 Quantum Statistics: Bose-Einstein and Fermi-Dirac Statistics
7.5 Bosons and fermions ideal gases
8. Bosons and fermions ideal gases
8.1 Bosons gases.
Photons. Black-body radiation
Phonons. Heat capacity of the crystal lattice
Bose-Einstein condensation
8.2 Fermion gases.
Heat capacity of electrons
Degeneration pressure of fermions
9. Elementary kinetic theory of gases
9.1. Gas diluted in equilibrium
9.2. Transport coefficients
Thermal conductivity of the crystal lattice and electrons
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Personal work | 57 | 2.28 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 |
| Group work | 25 | 1 | 1, 2, 4, 6, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 |
| Theory Classes | 33 | 1.32 | 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37 |
| Delivery activities | 10 | 0.4 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 |
| Exercises classes | 16 | 0.64 | 1, 2, 3, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37 |
Master classes
The teacher will explain the content of the syllabus with the support of audiovisual material that will be available to students in the Virtual Campus web in advance, at the beginning of each course topic. It is recommended that students have this material at hand in order to follow the classes more easily. Classes combine the use of slides with developments on the board. Student participation in class will be promoted. The teacher will solve some practical examples to illustrate the theory.
Problem Classes
The teacher will solve selected problems from the list that they will find on the Virtual Campus and students will solve in class some problems in groups. In previously established dates, students in groups of 3 students will deliver resolved problems (one delivery per group).
Some sessions will be devoted to the use of simulation tools. Students will make a simple code and analyze simulation results.
If a group believes that there is a participant who has not worked reasonably equitable, it can be expelled from the group.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Exercises and projects delivery | 25% | 0 | 0 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37 |
| Resit Exam | 75% | 3 | 0.12 | 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 |
| Partial Exams | 75% | 6 | 0.24 | 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 |
1. Group work. It consists of solving selected exercises (in groups of 3 students) and some numerical simulations (in groups of 2 students). The score in this evaluation group represents 25% of the final (individual) grade
2. Individual assesment: this part assess individually scientific and technical knowledge of the subject achieved by the student, as well as its capacity for analysis, synthesis and critical reasoning. It will consist of:
Partial exams: 75%.
Resit exam: 75%. It includes all the syllabus of the course (not each partial separately).
Important: In order to average the grade of the exam with the other 25%, the average score of the exams must be greater than or equal to 4 in a scale of 10.
Resit exam: in order to attend the retake exam the student must have attended the two partial exams.
Those students who pass the partial tests can attend the resit exam to improve the grade. If the score got in the resit exam is up to 1.5 points lower than the average partials score, it is kept the average partials score (unless it is less than 4). If you think you will not upgrade the score, you may not deliver the exam.
Not Assessable: The Not Assessable qualification will be obtained if the student does not attend any exam.
UNIQUE ASSESSMENT
Students who have accepted the single assessment modality will have to take a final test which will consist of a written exam that including problem solving and some theoretical questions. This test will take place on the same day as the second continuous assessment exam. Upon completion, students will deliver all deliverables and simulation reports.
The final grade is obtained in the same way as the continuous assessment: the exam weighs 75% of the final grade and the deliveries 25%.
Important: To average with the other 25% of the grade, the score of the exam must be 4 out of 10 or higher.
If the exam grade does not reach 4 or the final grade does not reach 5, the student has another opportunity to pass the subject through the recovery exam that will be held on the date set by the coordination of the qualification. The same recovery system will be applied as for the continuous assessment: the part of the grade corresponding to theory and problems (75%) can be recovered, the deliveries do not.
Bibliography
Basic
- R.K. Pathria, Statistical Mechanics, (3rd Ed), Academic Press, 2011.
- K. Huang, Introduction to statistical physics,Boca Raton, CRC Press, 2001
- F. Reif, Física estadística. Barcelona, Reverté, 1969
- J. Ortín, J.M. Sancho, Curso de Física Estadística, Barcelona, Publicacions i Edicions de la Universitat de Barcelona, cop. 2006
Advanced
- D. A. McQuarrie, Statistical Mechanics. University Science Books, cop. 2000.
- D.J. Amit and Y. Verbin, Statistical Physics: An introductory course. Singapore, World Scientific, 1995.
- D. Chandler, Introduction to Modern Statistical mechanics. Oxford, New York, 1987
- C. Fernandez, J.M. Rodríguez Parrondo, 100 problemas de Física Estadística, Madrid, Alianza, 1996
- R. Kubo. Statistical Mechanics: an advanced course with problems and solutions. Amsterdam, North-Holland, 1990.
- K.A. Dill and S. Bromberg. Molecular driving forces: Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience. Garland Science; 2nd edition, 2010.
Specialized articles and Web links
You will find them in the Virtual Campus
Software
There is no specific software for the subject
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TE) Theory | 1 | Catalan/Spanish | first semester | morning-mixed |
| (PAUL) Classroom practices | 1 | Catalan/Spanish | first semester | morning-mixed |