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Efektivna teorija difuzije
ID Pelaič, Jaka (Author), ID Grozdanov, Sašo (Mentor) More about this mentor... This link opens in a new window

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Abstract
V delu obravnavamo difuzijo s sodobnega vidika efektivne teorije polja. Najprej predstavimo Schwinger-Keldyshev formalizem za izračun realnočasovnih korelatorjev, preučimo njihove lastnosti in nato s pomočjo pridobljenih spoznanj formuliramo efektiven opis mikroskopskih sistemov s popotnimi integrali. Tako dobljeno efektivno teorijo analiziramo najprej v splošnih potezah – dokažemo na primer, da tudi na perturbativnem nivoju velja t.i. enačba največjega časa – nato pa jo analiziramo še kvantitativno. Določimo splošno obliko efektivne akcije v prvem redu v odvodih, a v vseh redih v poljih, iz katere perturbativno izračunamo popravke na nivoju ene zanke in klasificiramo vse diagrame, ki prispevajo na nivoju dveh zank.

Language:Slovenian
Keywords:difuzija, efektivna teorija polja, hidrodinamika, akcijski princip, korelacijske funkcije, Schwinger-Keldyshev formalizem, enačba največjega časa, KMS pogoj, fluktuacijsko-disipacijski izrek, perturbativni razvoj, Dysonova vrsta, Feynmanovi diagrami
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2022
PID:20.500.12556/RUL-142013 This link opens in a new window
COBISS.SI-ID:125700355 This link opens in a new window
Publication date in RUL:15.10.2022
Views:430
Downloads:108
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Secondary language

Language:English
Title:Effective theory of diffusion
Abstract:
In this work we treat diffusion with the modern tools of effective field theory. We first present the Schwinger-Keldysh formalism for evaulating real-time correlators, study their properties and then use the insights gained to formulate an effective description of microscopic systems via the path integral formalism. We analyze the theory so obtained, first in broad strokes – for example, we prove the so-called largest time equation at the perturbative level – and then quantitatively. We determine the general form of the effetive action at first derivative order but at all orders in fields, then perturbatively compute the one-loop corrections and classify all two-loop diagrams.

Keywords:diffusion, effective field theory, hydrodynamics, action principle, correlation functions, Schwinger-Keldysh formalism, largest time equation, KMS condition, fluctuation-dissipation theorem, perturbative expansion, Dyson series, Feynman diagrams

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