Mathematical physics

Enrollment into the program.

Dimensions and units in physics, dimensional analysis and non-dimensionalizing computations. Mathematical functions of one and more variables, differentials, extrema, integrals.
Probability calculus and statistics. Distributions, definitions of probability, event, random variable. Transformation of random variables, Dirac delta function, joint probability, conditional probability, examples of important special probability distributions, expectation values and moments, correlation coefficient, measuring parameters of distributions and basics of statistics.
Vector calculus. Vector and scalar quantities in physics, coordinate systems and transformations of coordinates, dot and cross products. Vector fields, gradient, divergence and curl. Examples from electromagnetism.
Differential equations. Phase space, phase diagram, first order ordinary differential equations, stationary profiles, newton’s law, linearized motion of coupled oscillators. Partial differential equations: examples for the heat equation and vibration of a string.

I. Kuščer in A. Kodre, Matematika v fiziki in tehniki, DMFA 2006.

Students get acquainted with practical applications of the techniques of mathematical analysis and algebra for problem solving in physics.

The new knowledge should help the student to become independent in solving theoretical computational problems in physics, and to be able to precisely mathematically formulate problems coming from everyday life or from precise observations.

Lectures and problem solving excercises.
Student should pass a written exam, and after that she/he obtains an individual project problem excercise. A positive evaluation of the oral defense of the report on this project is the final condition for passing the course.
Grading: 1-5 (fail), 6-10 (pass)

Written exam
Project

[1] GORIN, Thomas, PROSEN, Tomaž, SELIGMAN, Thomas H., ŽNIDARIČ, Marko. Dynamics of Loschmidt echoes and fidelity decay. Physics reports, ISSN 0370-1573. [Print ed.], 2006, 435, nos. 2-5, str.3-156. [COBISS-SI-ID 1972068]
[2] PROSEN, Tomaž, ŽNIDARIČ, Marko. Matrix product simulations of non-equilibrium steady states of quantum spin chains. Journal of statistical mechanics, ISSN 1742-5468, 2009, no. 2, str. P02035-1-P02035-19. [COBISS-SI-ID 2150756]
[3] PROSEN, Tomaž. Open XXZ spin chain : nonequilibrium steady state and strict bound on ballistic transport. Physical review letters, ISSN 0031-9007. [Print ed.], 2011, vol. 106, issue 21, str. 217206-1-217206-4. [COBISS-SI-ID 2347108]
[4] ILIEVSKI, Enej, PROSEN, Tomaž. Thermodynamic bounds on Drude weights in terms of almost-conserved quantities. Communications in Mathematical Physics, ISSN 0010-3616, 2013, vol. 318, no. 3, str. 809-830. [COBISS-SI-ID 2535524]
[5] PROSEN, Tomaž. Exact nonequilibrium steady state of an open Hubbard chain. Physical review letters, ISSN 0031-9007. [Print ed.], 2014, vol. 112, iss. 3, str. 030603-1-030603-5. [COBISS-SI-ID 2636644]