Course: Low-Dimensional Physical Systems

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Course title Low-Dimensional Physical Systems
Course code OPT/PGSFS
Organizational form of instruction Lecture
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 15
Language of instruction Czech, English
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Bajer Jiří, prof. RNDr. CSc.
  • Hradil Zdeněk, prof. RNDr. CSc.
Course content
-Basic electron-phonon models in one dimension and two dimensions, structural instability: Holstein's model, Peierls's model and Jahn-Teller model -Solitons as quasi-particles in low-dimensional physics (polymers, quasi-one-dimensional structures): Concept of soliton and solitary wave, basic types of the soliton-bearing nonlinear equations -Sine-Gordon model, domain walls -Instantons and their applications in the tunneling transport -Davydov's soliton, nonlinear Schrödinger equation -Mathematical methods of soliton solution analysis: Classical solitons of the sine-Gordon system -Quantization of static solutions, spectra of bound states, mass of quantum soliton, stability of solitons -Collective coordinates, zero mode, some examples of soliton analytical solutions in collective coordinates -Universality of systems with the SU(2) symmetry: Bosonization

Learning activities and teaching methods
Dialogic Lecture (Discussion, Dialog, Brainstorming)
Learning outcomes
Basic electron-phonon models in one dimension and two dimensions, structural instability
Evaluation Evaluate the particular methods and principles, explain the aspects and results concerning the given issue, integrate the knowledge, predict the solutions, evaluate the results and outcomes.
No prior requirements.

Assessment methods and criteria
Oral exam

Knowledge within the scope of the course topics (examination)
Recommended literature
  • Haken, H. (1987). Kvantovopoľová teória tuhých látok. ALFA, Bratislava.
  • Rajaraman, R. (1982). Solitons and Instantons. North-Holland Publishing Company, Amsterdam.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester