# Statistical physics

2022/2023
Programme:
Physics, Second Cycle
Orientation:
Astrophysics
Year:
2 year
Semester:
first
Kind:
optional
ECTS:
8
Language:
slovenian
Lecturers:
Hours per week – 1. semester:
Lectures
3
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)

Basic concepts of statistical physics:
Density matrix, partition function, thermodynamic averages. Entropy and microcanonical ensemble: reversibility, egodicity, typicality. Legendre transforms and thermodynamic potentials. Canonical and grandcanonical distribution. Quantum statistics: fermions, bosons, anyons. Fermi gas, Bose-Einstein condensation.

Theory of phase transitions:
Classification (continous and discontinous transitions), analyticity of thermodynamic potentials, order parameter, symmetries. Quantum phase transitions, topological phases (Kitaev model). Existence of phase transitions: Mermin-Wagner theorem, Perron theorem. Solvable models: 1D and 2D Ising. Critical exponents and universality. Mean field approximation, Landau theory,
Ginzburg criterium. Renormalization group theory in real space: examples of 1D and 2D Ising.
Non-equilibrium statistical physics:
Linear response theory: response function, fluctuation-dissipation theorem; calculation of transport coefficients – an example of electrical conductivity. Symmetries of transport coefficients, Onsager relations. Stochastic processes: Langevin equation, Brownian motion, gaussian processes, Fokker-Planck equation. Nonequilibrium fluctuation theorems: Tasaki - Crooks theorem , Jarzynski equality, generalization of the II. Law of thermodynamics. Systems far from equilibrium: master equations, principle of detailed balance, stationary states, exclusion models.

Izbrana poglavja iz učbenikov:
F. Schwabl, Statistical Mechanics (Springer, Berlin, 2002).
K. Huang, Statistical Mechanics (John Wiley & Sons, New York, 1987).
P. Papon, J. Leblond in P. H. E. Meijer, The Physics of Phase Transitions (Springer, Berlin, 2002).
J.M. Yeomans, Statistical Mechanics of Phase Transitions (Clarendon Press, Oxford, 1992).
N. Goldenfeld, Lectures on phase transitions and the renormalization group (Addison-Wesley, Urbana-Champain, 1992).
M. Le Bellac, F. Mortessagne in G. G. Bartrouni, Equilibrium and Non-Equilibrium Statistical Thermodynamics (CUP, Cambridge, 2010).
N. Pottier, Nonequilibrium Statistical Physics (Oxford University Press, Oxford, 2010).

Objectives and competences

Application of methods of statistical physics for description and analysis of equilibrium and non-equilibrium phenomena.

Intended learning outcomes

Knowledge and understanding:
Basic understanding of concepts in statistical physics, phase transitions and lattice models.

Application:
The analysis of equilibrium and non-equilibrium phenomena using the methods of statistical physics.

Reflection:
Critical evaluation of theoretical predictions using experimental results.

Transferable skills:
Understanding of phenomena and their explanation using experimental results.

Learning and teaching methods

Lectures, seminar excercises, home work, tutorial.

Assessment

Written exam
Oral exam.
grading: 1-5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Spin thermopower in interacting quantum dots,
T. Rejec, R. Žitko, J. Mravlje, and A. Ramšak, Phys. Rev. B 85, 085117 (2012).

Exact nonadiabatic holonomic transformations of spin-orbit qubits,
T. Čadež, J.H. Jefferson, and A. Ramšak, Phys. Rev. Lett. 112, 150402 (2014).

Effect of assisted hopping on thermopower in an interacting quantum dot,
S.B. Tooski, A. Ramšak, B.R. Bulka, and R. Žitko, New J. Phys. 16, 055001 (2014).

Exact large-deviation statistics for a nonequilibrium quantum spin chain, M. Žnidarič, Phys. Rev. Lett. 112, 040602 (2014).