1. SylabUZ
2. Wydział Nauk Ścisłych i Przyrodniczych
3. semestr zimowy 2024/2025
4. WFiA - oferta ERASMUS - Program Erasmus
5. Statistical Physics

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Statistical Physics - opis przedmiotu

Cel przedmiotu

The aim of the course is to familiarize students with the main issues of statistical physics which connects the microscopic and macroscopic worlds and constitutes the basis of thermodynamics. At the same time, the student should acquire the ability to understand and accurately describe various physical phenomena.

Wymagania wstępne

Zapisz zmiany

Passed courses "Fundamentals of Physics I, II” and “Quantum Physics I”

Zakres tematyczny

Lecture:

- Thermodynamics: concept of thermodynamic state, extensive and intensive variables, heat, work and internal energy, the first law of thermodynamics, concepts of entropy and temperature, Carnot engine, second law of thermodynamics, the fundamental equation, thermodynamic potentials: enthalpy, Helmholtz potential and Gibbs potential, the Legendre transformation, an ideal gas, the van der Waals system;

- Phase transitions: critical phenomena, the Clausius-Clapeyron equation, the order parameter, critical fluctuations, scale invariance and critical exponents, universality;

- Kinetic theory: kinetics of classical ideal gas, the Maxwell–Boltzmann velocity distribution, degrees of freedom and the equipartition theorem, the Boltzmann equation, the H-theorem and irreversibility, the kinetic theory vs statistical mechanics;

- Classical statistical mechanics: the ergodic hypothesis, the microcanonical ensemble, the thermodynamic limit, the thermal bath and canonical ensemble, the partition function, energy fluctuations, the grand canonical ensemble, the equivalence of thermodynamic ensembles, the Ising model and its applications;

- Quantum statistical mechanics: the Bose-Einstein and Fermi-Dirac statistics, pure and mixed states in quantum statistical mechanics, density matrix, the second quantization, quantum canonical ensembles, quantum ideal gases, the Debye model of vibrations;

 

Class:

- Termodynamics: thermodynamic processes, Carnot cycle, entropy in practical issues, equations of state for gases, magnetic systems and elastic systems, thermal equilibrium, specific heat;

- Phase transitions: critical phenomena for gases, magnetic systems and binary liquid mixtures

- Kinetic theory: mean square velocity of gas molecules and its relationship with gas temperature and pressure, mean free path, Maxwell velocity distribution, non-equilibrium processes;

- Classical statistical mechanics: the Gibbs paradox, thermodynamic potentials and their relations, partition functions and thermodynamic quantities, the one-dimensional Ising model, a simple model of paramagnet;

- Quantum statistical mechanics: the Fermi-Dirac and Bose-Einstein distributions, the occupation number formalism, the blackbody radiation, quantum harmonic oscillators, the electron gas;

Metody kształcenia

Classes are in the form of lectures where the student is encouraged to ask questions. On the exercises, students analyze and solve problems with a teacher.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

The exam is conducted in writen form. Student receives four issues to consider that require the knowledge of the issues and ability to combine various phenomena. For each task, one can receive from 0 to 5 points. To obtain a positive grade it is necessary to obtain at least 8 points (sufficient for 8-10.5 points, plus sufficient for 11-13.5 points, good 14-16, plus good 16.5-18.5 points, very good 19-20 points).

The basis of assessment exercises is attendance and passing written tests.

 

The classes must be completed before the exam begins.

The final grade is a weighted grade from two parts: exercises (40%) and final exam (60%).

Literatura podstawowa

[1] M. Kardar, „Statistical Physics of Particles”, Cambridge University Press, New York, 2007

[2] L. Peliti, „Statistical Mechanics in a Nutshell”, Princeton University Press, 2011

[3] M. Plischke and B. Bergesen, „Equilibrium Statistical Physics”, World Scientific, Singapore, 1994

Literatura uzupełniająca

[1] M. Gitterman, V. Halpern, Phase transitions. A Brief Account with Modern Applications, World Scientific 2004.

[2] R K Pathria , P. D. Beale, „Statistical Mechanics”, Elsevier, Amsterdam, 2011

[3] B. Poirier, „A conceptual guide to thermodynamics”, John Wiley & Sons Ltd, UK, 2014

[4] F. Reif, „Fundamentals of Statistical and Thermal Physics”, McGraw-Hill, New York, 1965

[5] J. P. Sethna, “Entropy, Order Parameters, and Complexity”, Oxford, 2006

[6] J. M. Yeomans, “Statistical Mechanics of Phase Transitions”, Oxford Science Publications, 1992

Uwagi

Zmodyfikowane przez dr Marcin Kośmider (ostatnia modyfikacja: 30-04-2024 15:29)