Dynamic properties of the excited states of matter

Lectures: 52 hours

Practical work: 20 hours

Work out of educational audience: 72 hours

2 master course (3 term)
2 master course (4 term)
Academics: 
Course program: 

1. Co-ordinate representation of operator of energy for the electronic states of solid and choice of the base system of wave functions. Operators of occupation and release (or births and destruction) of the electronic states. Transformation of operator of energy for the electronic states into representation of numbers of occupation (into representation of the second quantization or field representation).
2. Wave functions in representation of numbers of occupation. Different vacuum states.
3. Different types of excitations and its wave functions in representation of numbers of occupation.
3.1. The single-particle excitations. The electrons injected in a semiconductor. Frenkel excitons in molecular crystals. The excitonic operators of birth and destruction of excitations. Heitler-London approximation. Interaction of the excitations with a lattice. General dynamic properties of the single-particle excitation. General dynamic properties of classic dual soliton (soliton in a crystal). Dynamic properties of quasi-particle in the external field.
3.2. Two-particle excitation. Approximation of the weakly-coupled an electron and hole (charges are infinitely far from one another). Approximation of the strongly-coupled an electron and hole. Wannier-Mott excitons. Solitons on the base of Wannier-Mott excitons. Influence of the internal (excitonic) state on the structure of soliton shell. Thin structure of excitonic spectrums caused by auto-localisation.

Knowledge tests: 

Examination.

Literature: 

1. Х. Хакен. Квантовополевая теория твердого тела. М.: Наука, 1980.
2. А. С. Давыдов. Теория молекулярных солитонов. М.: Наука, 1968.
3. А. М. Косевич, Б. А. Иванов, А. С. Ковалев. Нелинейные волны намагниченности. Динамические и топологические солитоны. К.: Наукова думка, 1983.
4. А. С. Давыдов. Солитоны в молекулярных системах. К.: Наукова думка, 1988.
5. А. С. Давыдов. Теория твердого тела. М.: Наука, 1976.
6. А. А. Еремко, А. И. Сергиенко. К теории солитонов в молекулярных цепях. ФТТ, 1982, 24, № 12, с. 3720 – 3722.
7. A. D. Suprun. Two types of soliton solution of Schroedinger equation with the total nonlinearity of 5th degree. Functional Materials, 2001, 8, № 3, p. 436 – 441.
8. A. D. Suprun. Self-accelerating Painleve-II soliton: a curious mathematical trick or fundamental physics? Functional Materials, 2002, 9, № 3, p. 389 – 394.
9. А. Д. Супрун. Квантова теорія конформаційних збуджень білкових молекул. К.: ВПЦ "Київський університет". 2005. 117 с.
10. І. П. Пінкевич, В. Й. Сугаков. Теорія твердого тіла. Навчальний посібник. К.: ВПЦ “Київський університет”. 2006. 333с.