Hämmerling, Jens:
Collective motion in quantum many-body systems
Duisburg, Essen, 2011
2011dissertation
Physics (incl. Astronomy)Faculty of Physics
Title in English:
Collective motion in quantum many-body systems
Author:
Hämmerling, JensUDE
LSF ID
49351
Other
connected with university
Thesis advisor:
Guhr, ThomasUDE
GND
1055751025
LSF ID
47801
ORCID
0000-0002-0927-6324ORCID iD
Other
connected with university
Place of publication:
Duisburg, Essen
Year of publication:
2011
Extent:
97 S.
DuEPublico 1 ID
Library shelfmark:
Note:
Duisburg, Essen, Univ., Diss., 2011
Language of text:
English

Abstract in English:

We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transition strengths induced by the collective mode is determined by its classical dynamics. This allows us to derive the spreading for the collective coordinate from first principles. After that we study the interplay between collective and incoherent single--particle motion in a model of two chains of particles whose interaction comprises a non--integrable part. In the perturbative regime, but for a general form of the interaction, we calculate the Fourier transform of the time correlation for the collective coordinate. We obtain the remarkable result that it always has a unique semi-classical interpretation. We show this by a proper renormalization procedure which also allows us to map the non-integrable system to the integrable model of Caldeira--Leggett--type considered previously in which the bath is part of the system.