dc.contributor.author | Säkkinen, Niko | |
dc.date.accessioned | 2017-02-21T08:16:10Z | |
dc.date.available | 2017-02-21T08:16:10Z | |
dc.date.issued | 2016 | |
dc.identifier.isbn | 978-951-39-6814-4 | |
dc.identifier.other | oai:jykdok.linneanet.fi:1673703 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/53076 | |
dc.description.abstract | In this thesis, an approximate method introduced to solve time-dependent many-body problems
known as time-dependent many-body perturbation theory is studied. Many-body perturbation theory
for interacting electrons and phonons is reviewed. In particular, the electron propagator G and an
unconventional two-component phonon propagator, which satisfy coupled integral Dyson equations,
are introduced. In practice, the associated integral kernels known as the electron Σ and phonon
self-energies need to be approximated. The conserving approximations known as the Hartree (-Fock)
and the ﬁrst and second Born approximations, which respect the continuity equation between the
electron density and current, are considered in this work.
Time-dependent systems of interest are studied in this thesis by using the integro-diﬀerential forms
of the Dyson equations referred to as the Kadanoﬀ-Baym Equations (KBE). The Kadanoﬀ-Baym
equations are introduced for the electron and phonon propagators unconventionally as coupled ﬁrstorder integro-diﬀerential equations. It is reviewed how these equations are solved numerically by
describing an integration rule, a class of practical methods and a parallel implementation of the
numerical method. In addition, documentation of how the Kadanoﬀ-Baym equations allow to solve
the Bethe-Salpeter Equation (BSE) with the kernel δΣ/δG for the density response function, is
provided.
In two of the enclosed publications, we benchmarked observables obtained by using the Hartree and
partially and fully self-consistent Born approximations against numerically exact results for the two-
site, two-electron Holstein model. In this model, the two electrons which are constrained to move
between two lattice sites interact indirectly via the electron-phonon coupling. It was observed that
only the fully self-consistent Born approximation could cope qualitatively correctly with the competition between the delocalizing and localizing eﬀects of the kinetic and interaction energies. For the
other two approximations, spurious bifurcative symmetry breaking with an associated unbounded
density response was observed. Nevertheless, also the self-consistent Born approximation was concluded to fail in describing the bipolaronic behavior of the true system. In the third publication,
we benchmarked the Hartree-Fock and second Born approximations against an exact method for
the few-site Hubbard and Pariser-Parr-Pople models in which the underlying lattice is inert and the
electrons interact amongst themselves directly. It was found that the second Born approximation is
capable of describing the so-called correlation induced doubly-excited states. This is not possible for
time-local approximations such as Hartree-Fock.
In addition to the qualitative results, which highlight successes of the applied simple self-energy approximations, the approximate and exact results were also compared on a more quantitative level. It
is the quantitative and qualitative results combined which are used in this thesis to assess the quality
of the many-body approximations used, with the aim to better understand when these methods are
predictive. | |
dc.format.extent | Verkkoaineisto (xii, 160 sivua) | |
dc.language.iso | eng | |
dc.publisher | University of Jyväskylä | |
dc.relation.ispartofseries | Research report / Department of Physics, University of Jyväskylä | |
dc.relation.isversionof | Julkaistu myös painettuna. | |
dc.subject.other | monen kappaleen teoria | |
dc.subject.other | aikariippuva monihiukkashäiriöteoria | |
dc.subject.other | Greenin funktio | |
dc.subject.other | many-body problems | |
dc.subject.other | many-body theory | |
dc.subject.other | time-dependent many-body perturbation theory | |
dc.subject.other | Green's function | |
dc.subject.other | electron-phonon interaction | |
dc.subject.other | excitation spectra | |
dc.title | Application of time-dependent many-body perturbation theory to excitation spectra of selected finite model systems | |
dc.type | Diss. | |
dc.identifier.urn | URN:ISBN:978-951-39-6814-4 | |
dc.type.dcmitype | Text | en |
dc.type.ontasot | Väitöskirja | fi |
dc.type.ontasot | Doctoral dissertation | en |
dc.contributor.tiedekunta | Matemaattis-luonnontieteellinen tiedekunta | fi |
dc.contributor.tiedekunta | Faculty of Mathematics and Science | en |
dc.contributor.yliopisto | University of Jyväskylä | en |
dc.contributor.yliopisto | Jyväskylän yliopisto | fi |
dc.contributor.oppiaine | Fysiikka | fi |
dc.relation.issn | 0075-465X | |
dc.relation.numberinseries | 2016, 15 | |
dc.rights.accesslevel | openAccess | fi |
dc.subject.yso | kiinteän olomuodon fysiikka | |
dc.subject.yso | kvanttimekaniikka | |
dc.subject.yso | numeeriset menetelmät | |
dc.subject.yso | approksimointi | |
dc.subject.yso | elektronit | |
dc.subject.yso | fononit | |
dc.subject.yso | spektroskopia | |