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Correlations in Many-Electron Systems - NFPL551

Title:	Korelace v mnohoelektronových systémech
Guaranteed by:	Department of Condensed Matter Physics (32-KFKL)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Note:	course can be enrolled in outside the study plan enabled for web enrollment

Guarantor:	Mgr. Jindřich Kolorenč, Ph.D.

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KFES (15.05.2014)

At the start of the course we recall the Hartree–Fock approximation that, apart from the Pauli principle, neglects all other correlations among particles. Using applications to a few simple systems we illustrate the accuracy as well as the weaknesses of this approximation. For the ground state of the helium atom we construct a considerably more accurate wave function that takes into account correlations among the two electrons and that still allows for evaluation of the approximate ground-state energy by analytical means. Numerical methods will applied for analogous correlated wave functions.

Literature

Last update: Mgr. Jindřich Kolorenč, Ph.D. (29.04.2019)

1. A. Szabo, N. S. Ostlund, Modern quantum chemistry, Dover Publications, 1996

2. G. F. Giuliani, G. Vignale, Quantum theory of the electron liquid, Cambridge Univer-

sity Press, 2005

3. E. A. Hylleraas, Neue Berechnung der Energie des Heliums im Grundzustande, sowie

des tiefsten Terms von Ortho-Helium, Z. Physik 54, 347-366 (1929); anglický pre-

klad je soucástí H. Hettema, Quantum chemistry: Classic scientic papers, World

Scientic, 2000

4. B. L. Hammond, W. A. Lester, jr., P. J. Reynolds, Monte Carlo methods in ab initio

quantum chemistry, World Scientic, 1994

5. I. Kosztin, B. Faber, K. Schulten, Introduction to the diffusion Monte Carlo method,

Am. J. Phys. 64, 633-644 (1996)

6. J. Kolorenc, L. Mitas, Applications of quantum Monte Carlo methods in condensed

systems, Rep. Prog. Phys. 74, 026502 (2011)

Syllabus -

Last update: Mgr. Jindřich Kolorenč, Ph.D. (29.04.2019)

1. Hartree-Fock approximation: elementary properties and weaknesses, preference

of magnetically ordered states, spin contamination; illustrations on the hyd-

rogen molecule and homogeneous phases of the electron gas; Overhauser’s

theorem (optional)

2. helium atom and helium-like ions: analytical properties of the many-body wave

functions in Coulomb systems, Hylleraas’ variational method (or how to hold

together the negative hydrogen ion with just a pen and paper), amount of

correlations in orthohelium and parahelium

3. variational Monte Carlo: Jastrowcorrelation factor, evaluation of quantum-mecha-

nical expectation values by means of stochastic integration, Metropolis algori-

thm for generation of random numbers with complicated multivariate distri-

butions, elementary properties of Markov chains (that represent the basis of

the Metropolis algorithm)

4. diffusion Monte Carlo: projection of the exact ground state from an approximate

solution, Feynman-Kac formula, stochastic evaluation of the path integral,

fermion sign problem, examples of applications