TY - BOOK

T1 - On the Second Order Correction to the Ground State Energy of the Dilute Bose Gas

AU - Brietzke, Birger

PY - 2017

Y1 - 2017

N2 - In this thesis we consider a gas of interacting, identical, spin-less bosons in a thermodynamic box.We are interested in the ground state energy, which for low densities (diluteness) is described bythe Lee{Huang{Yang (LHY) formula { a series expansion in the density that has been derivedfrom Bogolubov's work in the late 1950's.In the introduction we discuss how to derive the LHY formula using Bogolubov's approximationstep, which presupposes Bose-Einstein condensation. The second part contains a detailed proof,which establishes the LHY formula as a lower bound in a weak coupling and low density regime.While our proof is guided by Bogolubov's predictions, it is based on a two-step localizationprocedure, which allows us to prove adequate 'local condensation'.

AB - In this thesis we consider a gas of interacting, identical, spin-less bosons in a thermodynamic box.We are interested in the ground state energy, which for low densities (diluteness) is described bythe Lee{Huang{Yang (LHY) formula { a series expansion in the density that has been derivedfrom Bogolubov's work in the late 1950's.In the introduction we discuss how to derive the LHY formula using Bogolubov's approximationstep, which presupposes Bose-Einstein condensation. The second part contains a detailed proof,which establishes the LHY formula as a lower bound in a weak coupling and low density regime.While our proof is guided by Bogolubov's predictions, it is based on a two-step localizationprocedure, which allows us to prove adequate 'local condensation'.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122404372605763

M3 - Ph.D. thesis

BT - On the Second Order Correction to the Ground State Energy of the Dilute Bose Gas

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -