Učni načrt predmeta

Vsebina:

Content (Syllabus outline):

1) Predstavitev poglavitnih tekoče-kristalnih (TK) faz.
2) Zlom simetrije in umeritveno polje.
3) Topološki defekti (TD):
- TD v TK v orientacijski in translacijski urejenosti,
- topološki naboj: univerzalna definicija,
- analogije med TD v TK in drugih področjih fizike (magnetni monopol, kozmične strune, vorteksi v superprevodnikih in supertekočinah, skyrmioni v fiziki delcev in magnetizmu, robne in zvite dislokacije v trdni snovi….).
4) Vpliv geometrije “prostora” na TD:
- univerzalni pomen Gaussove ukrivljenosti (Gauss-Bonnetov in Poincarejev teorem),
- vpliv ukrivljenosti “prostora” na lego TD,
- krivinsko inducirana tvorba parov defektantidefekt,
- koncept “paralenega transporta” in analogija s splošno teorijo relativnosti,
- stabilizacija mrež TD.
5) Anihilacija topoloških defektov:
- anihilacija TD v orientacijski in translacijski urejenosti TK,
- analogija z anihilacijo matematično sorodnih TD v kondenzirani materiji in delcev v fiziki osnovnih delcev.
6) Domenska struktura in zlom zvezne simetrije:
- anihilacija TD in rast domen,
- vpliv TD na sedanjo strukturo vesolja: Kibble-Zurkov mehanizem,
- univerzalni vpliv naključnega nereda na domensko strukturo: teorem Imry-Ma.
7) Univerzalni delčni opis narave z lokaliziranimi rešitvami pripadajočih ureditvenih polj.

1) Introduction of key liquid crystalline (LC) phases.
2) Symmetry breaking and gauge fields.
3) Topological defects (TD):
- TD in LCs in orientational and translational degree of ordering,
- topological charge: universal definition,
- analogy between TDs in LCs and other fields of physics (Dirac monopole, cosmic strings, vortices in superconductors and superfluids, skyrmions in particle physics and magnetism, edge and screw dislocations in condensed matter…).
4) Impact of curvature of “space” on TDs:
- universal role of Gaussian curvature (Gauss Bonnet and Poincare theorem),
- impact of curvature on position of TDs,
- curvature driven unbinding of pairs defectantidefect,
- concept of “parallel transport” and analogy with theory of general realativity,
- stabilisation of lattices of TDs.
5) Annihilation of TDs:
- annihilation of TDs in orientational and translational ordering in LCs,
- annihilation of mathematically analogous TDs in condensed matter physics and particle physics,
6) Domain structure and symmetry breaking:
- annihilation of TDs and domain growth,
- impact of TDs on structure of Universe: Kibble-Zurek mechanism,
- universal impact of random-type disorder on domain patterns: Imry-Ma theorem.
7) Universal “particle” description of nature in terms of localized solutions in relevant gauge fields.