Slobodna ekspanzija anyona

master's thesis

• Title (english): Free expansion of anyons
• Author: Katja Kustura
• Mentor: Hrvoje Buljan (mentor)
• Committee member: Hrvoje Buljan (predsjednik povjerenstva)
• Committee member: Danko Radić (član povjerenstva)
• Committee member: Mario Novak (član povjerenstva)
• Committee member: Damir Pajić (član povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2016-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Anyoni su čestice čija se svojstva kontinuirano interpoliraju između bozona i fermiona, a čije je postojanje teorijski dozvoljeno u dvodimenzionalnom svijetu. Prilikom zamjene dvaju anyona, njihova valna funkcija poprima proizvoljnu fazu e^iπα, gdje parametar α ∈ [0, 1] opisuje statistiku sustava (α = 0 odgovara Bose-Einsteinovoj, α = 1 Fermi-Diracovoj statistici). Razvoj eksperimentalnih metoda omogućio je realizaciju efektivno dvodimenzionalnih sustava zamrzavanjem stupnjeva slobode u trećoj dimenziji, što otvara mogućnost realizacije anyona kao kvazičestica u takvim sustavima. Glavna motivacija za proučavanje anyona je njihova potencijalna uloga u realizaciji topološkog kvantnog računala. U ovom radu proučena je dinamika neinteragirajućeg anyonskog sustava u kontekstu ultrahladnih atomskih plinova kao jedne od mogućih platformi za njihovu realizaciju. Analitički i numerički analizirana je slobodna ekspanzija anyonskog sustava iz svojstvenog stanja harmoničkog oscilatora, što je jedna od standardnih metoda za proučavanje svojstava atomskih plinova. Uočena je interpolacija jednočestične prostorne gustoće (SD) i raspodjele impulsa (MD) u ovisnosti o statističkom parametru α. Anyonska SD i MD nemaju isti oblik, za razliku od fermionskog i bozonskog slučaja. Dobivena je vremenska ovisnost tijekom slobodne ekspanzije, koja pokazuje samoslično ponašanje SD u vremenu, dok MD mijenja oblik i asimptotski postaje proporcionalna početnoj prostornoj gustoći. Promjena MD u vremenu je donekle iznenadujuća jer ona karakterizira interagirajuće sustave, i ukazuje na značajniju ulogu statistike čestica α u vremenskoj evoluciji sustava.

Abstract (english)

Anyons are particles with properties continuously interpolating from bosons to fermions, which are theoretically allowed to exist in a two-dimensional world. An exchange of two anyons causes the wave function to pick up a phase e^iπα, where the parameter α ∈ [0, 1] describes the statistics of the system (α = 0 corresponds to Bose-Einstein, and α = 1 to Fermi-Dirac statistics). Developments in experimental methods have enabled freezing out degrees of freedom in a system, thus creating effective two-dimensional systems. This opens up the possibility of realization of anyons as quasiparticles in such systems. The main motivation for studying anyons comes from their potential significance in fault-tolerant topological quantum computation. In this thesis, the dynamics of a non-interacting anyon system was studied in the context of ultracold atomic gases, as one of the possible platforms for their realization. Free expansion of anyons, one of the standard methods in studying atomic systems, was examined analytically and numerically. Interpolation of one-particle space density (SD) and momentum distribution (MD) in dependence on the statistical parameter α was obtained. Anyon SD and MD do not have the same shape, unlike bosonic and fermionic case. Time evolution during free expansion was obtained, and self-similar behavior of SD in time was observed, while anyonic MD changes shape with time and asymptotically becomes proportional to the initial SD. Change of MD in time is somewhat surprising, as it is a property of interacting systems, and indicates a greater role of statistics α in time evolution of the system.

• Keywords: anyoni; slobodna ekspanzija
• Keywords (english): anyons; free expansion
• Language: croatian
• URN:NBN: urn:nbn:hr:217:781541
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-03-04 15:32:57