@inproceedings{8044, abstract = {Many questions concerning models in quantum mechanics require a detailed analysis of the spectrum of the corresponding Hamiltonian, a linear operator on a suitable Hilbert space. Of particular relevance for an understanding of the low-temperature properties of a system is the structure of the excitation spectrum, which is the part of the spectrum close to the spectral bottom. We present recent progress on this question for bosonic many-body quantum systems with weak two-body interactions. Such system are currently of great interest, due to their experimental realization in ultra-cold atomic gases. We investigate the accuracy of the Bogoliubov approximations, which predicts that the low-energy spectrum is made up of sums of elementary excitations, with linear dispersion law at low momentum. The latter property is crucial for the superfluid behavior the system.}, author = {Seiringer, Robert}, booktitle = {Proceeding of the International Congress of Mathematicans}, isbn = {9788961058063}, location = {Seoul, South Korea}, pages = {1175--1194}, publisher = {International Congress of Mathematicians}, title = {{Structure of the excitation spectrum for many-body quantum systems}}, volume = {3}, year = {2014}, }