TY - BOOK

T1 - Analysis of the Bogoliubov free energy functional

T2 - a variational description of a weakly-interacting Bose gas

AU - Reuvers, Robin

PY - 2016

Y1 - 2016

N2 - In this thesis, we analyse a variational reformulation of the Bogoliubov approximation that is used todescribe weakly-interacting translationally-invariant Bose gases. For the resulting model, the `Bogoliubovfree energy functional', we demonstrate existence of minimizers as well as the presence of a phasetransition to Bose{Einstein condensation, and establish the phase diagram. We also give a calculation ofthe critical temperature assuming the gas is dilute, and nd that it agrees with earlier numerical studies.The thesis contains an introduction, a physical review paper outlining the main results and ideas,and two mathematical papers with detailed proofs

AB - In this thesis, we analyse a variational reformulation of the Bogoliubov approximation that is used todescribe weakly-interacting translationally-invariant Bose gases. For the resulting model, the `Bogoliubovfree energy functional', we demonstrate existence of minimizers as well as the presence of a phasetransition to Bose{Einstein condensation, and establish the phase diagram. We also give a calculation ofthe critical temperature assuming the gas is dilute, and nd that it agrees with earlier numerical studies.The thesis contains an introduction, a physical review paper outlining the main results and ideas,and two mathematical papers with detailed proofs

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99122937583405763

M3 - Ph.D. thesis

BT - Analysis of the Bogoliubov free energy functional

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

ER -