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master's thesis
Teorijski modeli prema eksperimentalnoj realizaciji anyona
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:680714
Štrkalj, Antonio
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

Cite this document

Štrkalj, A. (2016). Teorijski modeli prema eksperimentalnoj realizaciji anyona (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:680714

Štrkalj, Antonio. "Teorijski modeli prema eksperimentalnoj realizaciji anyona." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:680714

Štrkalj, Antonio. "Teorijski modeli prema eksperimentalnoj realizaciji anyona." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:680714

Štrkalj, A. (2016). 'Teorijski modeli prema eksperimentalnoj realizaciji anyona', Master's thesis, University of Zagreb, Faculty of Science, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:680714

Štrkalj A. Teorijski modeli prema eksperimentalnoj realizaciji anyona [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:217:680714

A. Štrkalj, "Teorijski modeli prema eksperimentalnoj realizaciji anyona", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:680714

Metadata
TitleTeorijski modeli prema eksperimentalnoj realizaciji anyona
Title (english)Theoretical models towards experimental realization of anyons
AuthorAntonio Štrkalj
MentorHrvoje Buljan (mentor)
Committee memberHrvoje Buljan (predsjednik povjerenstva)
Committee memberDanko Radić (član povjerenstva)
Committee memberMatko Milin (član povjerenstva)
Committee memberMario Novak (član povjerenstva)
Committee memberVito Despoja (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2016-07-15, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Za razliku od trodimenzionalnog prostora u kojem mogu egzistirati samo fermioni i bozoni, u dvodimenzionalnom svijetu možemo imati kvazičestice koje zadovoljavaju drugačiju statistiku. Prilikom zamjene dvije identične kvazičestice, valna funkcija dobiva fazni faktor eiπα gdje je α realni broj između 0 i 1. Stoga one nisu niti fermioni niti bozoni, već ih nazivamo anyonima. U ovom radu uveli smo pojam anyona preko jednostavnog primjera cilindara s tokom magnetskog polja Φ i česticom naboja q. To je najjednostavniji primjer anyona i njega je razmatrao Wilczek [5]. Jedini poznati efekt u prirodi koji pokazuje anyonska pobuđenja je kvantni Hallov efekt. Ostalih eksperimentalnih realizacija nema. Današnja istraživanja su usmjerena na mnogočestične sustave sa anyonskim pobuđenjima. Ovaj rad je različit od takvih pristupa jer su promatrane samo dvije čestice na koje smo nametnuli interakciju koja daje topološku fazu nakon zamjene čestica. Prva razmatrana interakcija je obična dipol-dipol za koju smo pokazali da ne daje topološku fazu. Njenom modifikacijom, izbacujući ovisnost o udaljenosti čestica iz interakcije, dobili smo topološku fazu nakon zamjene čestica, odnosno anyone. Pokazali smo da anyoni dobiveni takvom interakcijom nisu slobodni, već interagiraju potencijalom ovisnim o vanjskom magnetskom polju B i udaljenosti između čestica.
Abstract (english)
In three-dimensional space we can find only two types of particles regarding their statistics, fermions and bosons. When we restrict the system to two dimensions, different statistics can be obtained which is not necessarily purely fermionic or bosonic. Particles obeying that statistics are called anyons. Exchanging two identical anyons, wave function gets a phase factor eiπα where α can be any real number between 0 and 1. First we discuss the simplest model of anyons, originally discussed by Wilczek [5], where anyons are flux-tubes with magnetic flux Φ and charge q. The only known example of anyonic excitations in nature is fractional quantum Hall effect and no other experimental realization of anyons is achieved up to this date. Most of research is based on many-body systems with anyonic excitations, while this work has a different approach. We were using only two spin particles with imposed interaction to get topological phase after exchanging two identical particles. First interaction we considered was dipol-dipol interaction, not showing s topological phase. Modifying interaction by neglecting the dependency on distance between particles, we observed the topological phase. Anyons emerging from modified model are not free but interact via a potential which depends on external magnetic field B and the distance between anyons.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:680714
Study programmeTitle: Physics; specializations in: Research
Course: Research
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-03-05 12:13:51