Enrollment into the program.

# Advanced computational physics

Quantum physics:

simulation of time evolution in quantum mechanics, “split-step” (Suzuki-Trotter) decompositions of unitary operators – simplectic integrators

efficient diagonalization of large and sparse matrices: Lancoz, Arnoldi

basic concepts of random matrix theory and modelling of complex quantum systems,

density functional theory (DFT).

Statistična fizika (klasična in kvantna):

time evolution of classical statistical-mechanical systems, “molecular dynamics” simulations,

modelling of heat baths and stochastic differential equations: Langevin, Ohrnstein-Uhlenbeck processes,

Monte-Carlo methods, detailed balance and simulated annealing. examples: classical spin systems,

Quantum Monte-Carlo, simple examples, Feynman path-integral

numerical renormalization group methods (NRG, DMRG), examples: quantum spin chains, relaxation and thermalization

variational methods in matrix-product basis, area-laws, quantum entanglement, simulability.

W. G. Hoover, Computational Statistical Mechanics, (Elsevier 1991),

J. P. Sethna, Entropy, Order Parameters and Complexity (Oxford UP, 2006),

Quantum Simulations of Complex Many-Body Systems: From theory to algorithms (Lecture notes, ur. J. Grotendorst, D. Marx in A. Muramatsu), NIC Series, Vol 10 (2002).

U. Schollwoeck, The density-matrix renormalization group in the age of matrix product states, Annals of Physics 326 , 96-192 (2011)

Student should master some of the most basic and useful state-of-the art computational methods for simulation of simple (single particle, or linear), and complex (many particle, or non-linear) quantum or classical statistical systems.

Knowledge and understanding:

Mastering of advanced numerical methods and approaches to simulations of systems with many degrees of freedom in statistical and quantum physics.

Application:

Student should know how to apply the new knowledge in theoretical modelling and computer simulations of complex systems in physics

Reflection:

Student should get a feeling for what is possible to simulate efficiently in pysics and what not.

Transferable skills:

The methods and contents of the course have links to, or require some prior knowledge from courses on: statistical physics, theory of dynamical systems, solid state physics and advanced quantum mechanics.

Lectures, exercises, homework projects, consultations

Sucessful individual completion of six biweekly project homeworks, their discussion in the class and individual defence with professor/assistant

grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Prof. dr. Tomaž Prosen

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, doi: 10.1088/1742-5468/2009/02/P02035. [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, doi: 10.1103/PhysRevLett.106.217206. [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. http://download.springer.com/static/pdf/48/art%253A10.1007%252Fs00220-012-1599-4. pdf?auth66=1363681672_5113fee186b3d7c9c4df4b1c6a129545&ext=.pdf. [COBISS-SI-ID 2535524]

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. http://prl.aps.org/abstract/PRL/v112/i3/e030603. [COBISS-SI-ID 2636644