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Author:Häppölä, Juho
Title:XY-model, Unitary Equilibration and Lieb-Robinson Speed
XY-malli, ykseinen tasapainottuminen ja Lieb-Robinsonin nopeus
Publication type:Master's thesis
Publication year:2011
Pages:[6] + 51      Language:   eng
Department/School:Teknillisen fysiikan laitos
Main subject:Fysiikka (laskennallinen fysiikka)   (Tfy-105)
Supervisor:Ala-Nissilä, Tapio
Instructor:Hamma, Alioscia
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark Aalto  244   | Archive
Keywords:Loschmidt echo
unitarity
equilibration
statistical physics
quantum physics
quantum quensh
statistinen fysiikka
unitaarinen aikakehitys
tasapainottuminen
termalisaatio
Abstract (eng): We study the unitary equilibration of a chain of interacting spins described by quantum mechanical XV-model in a transverse field.
Using the exact solubility of the model we compute the behavior of the Loschmidt echo along with other observables when the system prepared far away from equilibrium in a quantum quench.
In a local system like the XV-model there is a maximal speed of information in the system, bounded by the Lieb-Robinson bound.
We argue that in the process of unitary equilibration observables fluctuate from their most probable value on a time scale given by the linear size of the system and the speed of interaction.
In this thesis, we demonstrate that this time scale is universal and not dependent on the specific details of the Hamiltonian nor the initial state of the system.
Furthermore, we provide evidence that suggests that our claims can be generalized to non integrable local systems as well.
Abstract (fin): Tutkimme vuorovaikuttavan spin-ketjun unitaarista aikakehitystä kohti tasapainotilaa.
Hyödyntäen kvanttimekaanisen XY-mallin eksaktia ratkeavuutta, johdamme lausekkeen Loschmidtin kaiulle tilanteessa jossa spin-ketju preparoidaan kauas tasapainotilastaan vaihtamalla systeemin Hamiltonin funktiota äkillisesti.
Lokaalisti vuorovaikuttaville kvanttisysteemeille on ominaista informaation kulun äärellinen nopeus, niinkutsuttu Lieb-Robinsonin nopeus.
Demonstroimme tässä opinnäytetyössä, kuinka unitaarisesti tasapainottuvan systeemin havainnoitavat suureet fluktuoivat poikkeuksellisen voimakkaasti aikaskaalalla, joka riippuu suoraan systeemin koosta ja Lieb-Robinsonin nopeudesta.
Lisäksi näytämme, että tämä aikaskaala on universaali, eikä riipu kvanttisysteemin tarkasta alkutilasta tai Hamiltonin operaattorin täsmällisistä parametreista.
Lisäksi esitämme numeerisia laskelmia, joiden perusteella vaikuttaa, että tuloksemme yleistyy myös integroitumattomille systeemeille.
ED:2011-12-21
INSSI record number: 43640
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