Seminarium KMMF "Teoria Dwoistości"

We consider a variational approach to the Bose-Hubbard model based onthe Bogoliubov theory. We introduce the free energy functional for whichwe prove the existence of minimizers. By analyzing their structure weshow the existence of a superfluid--Mott insulator phase transition atpositive temperatures. We also show that this model does not exhibit aquantum phase transition. Joint work with Marcin Napiórkowski.