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master's thesis
Modulacijska nestabilnost nelinearne Schrödingerove jednadžbe sa sintetskim magnetskim poljem
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:417678
Čelan, Ozana
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

Cite this document

Čelan, O. (2019). Modulacijska nestabilnost nelinearne Schrödingerove jednadžbe sa sintetskim magnetskim poljem (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:417678

Čelan, Ozana. "Modulacijska nestabilnost nelinearne Schrödingerove jednadžbe sa sintetskim magnetskim poljem." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:417678

Čelan, Ozana. "Modulacijska nestabilnost nelinearne Schrödingerove jednadžbe sa sintetskim magnetskim poljem." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:417678

Čelan, O. (2019). 'Modulacijska nestabilnost nelinearne Schrödingerove jednadžbe sa sintetskim magnetskim poljem', Master's thesis, University of Zagreb, Faculty of Science, accessed 24 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:417678

Čelan O. Modulacijska nestabilnost nelinearne Schrödingerove jednadžbe sa sintetskim magnetskim poljem [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 December 24] Available at: https://urn.nsk.hr/urn:nbn:hr:217:417678

O. Čelan, "Modulacijska nestabilnost nelinearne Schrödingerove jednadžbe sa sintetskim magnetskim poljem", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:417678

Metadata
TitleModulacijska nestabilnost nelinearne Schrödingerove jednadžbe sa sintetskim magnetskim poljem
Title (english)Modulation instability in the nonlinear Schrödinger equation with a synthetic magnetic field
AuthorOzana Čelan
MentorKarlo Lelas (mentor)
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2019-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Dinamika slabo međudjelujućih Bose Einsteinovih kondenzata i propagacija svjetlosti kroz nelinearan medij opisuju se nelinearnom Schrödingerovom jednadžbom. Modulacijska nestabilnost je fenomen karakterističan za sustave opisane tom jednadžbom i istraživan je u kontekstu Bose Einstein kondenzata i u kontekstu nelinearne optike. U novije vrijeme se razvijaju metode za kreiranje sintetskih magnetskih polja u tim sustavima u svrhu realizacije kvantnih emulatora. Mi smo u ovom radu teorijski istražili kako na modulacijsku nestabilnost utječe uvođenje homogenog sintetskog magnetskog polja u nelinearnu Schrödingerovu jednadžbu. Razvili smo dvije numeričke metode za vremensku evoluciju jednadžbe te pokazali da se modulacijska nestabilnost događa i u prisutnosti sintetskog magnetskog polja. Također, pokazali smo da će rezultati vremenske evolucije ovisiti o odabiru vektorskog potencijala s kojim opisujemo homogeno sintetsko magnetsko polje. Objasnili smo da do razlika u vremenskim evolucijama, za različite odabire vektorskog potencijala, dolazi zbog sintetskog električnog polja koje se javlja u trenutku uključivanja sintetskog magnetskog polja.
Abstract (english)
Dynamics of weakly interacting Bose Einstein condensates, and propagation of light through nonlinear media, are both described with the nonlinear Schrödinger equation. Modulation instability is a phenomenon characteristic for systems described with this equation and it was explored in the context of Bose Einstein condensates and in the context of nonlinear optics. Recently, new methods are being developed for creating homogeneous synthetic magnetic fields in these systems in order to create quantum emulators. In this work we theoretically explored how the implementation of the homogeneous synthetic magnetic field in nonlinear Schrödinger equation influences the modulation instability. We developed two numerical methods for the time evolution of the equation, and we showed that the modulation instability also occurs in the presence of homogeneous synthetic magnetic field. We also showed that the results of time evolution will depend on the choice of the vector potential used to describe the homogeneous synthetic magnetic field. We explained that the differences in time evolutions, for different choices of vector potential, occur because of the synthetic electric field which appears in the moment of activation of the homogeneous synthetic magnetic field.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:417678
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
Embargo expiration date: 2020-09-26
Terms of useLicence In copyright icon
Created on2020-01-07 10:08:03