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Reduced Density Matrix Functional Theory for Bosons

Authors: Jakob Wolff

Ref.: Master thesis, Martin-Luther University of Halle-Wittenberg (2020)

Abstract: It is the main goal of this thesis to confirm that an extension of reduced density matrix functional theory to bosonic systems is useful. and to show its huge potential of this theory. The thesis is structured as follows. The first chapter is concerned with the theoretical foundation of the thesis. This involves the basic notion of density operators and reduced density matrices as well as representability. Especially the key quantity of this work, the one-body reduced density matrix, will be introduced. In the second chapter, it will be shown that the energy of an interacting many-body system is a functional of the one-body reduced density matrix and thus its knowledge suffices to calculate the ground state energy of a system. The theory is called Reduced Density Matrix Functional Theory (RDMFT) and will be discussed extensively. Additionally, it is compared to the famous Density Functional Theory. All elaborated concepts of these two chapters will be discussed based on a the Bose-Hubbard dimer in the last chapter. The study of this model in the framework of bosonic RDMFT reveals a new physical concept, the so called Bose-Einstein force, which explains the phenomenon of quantum depletion in interacting bosonic many-body systems.