Calculus of Variations and Geometric Measure Theory
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Ground states and Excitation Spectrum of Bosonic Quantum Many-Body Systems

Robert Seiringer

created by gelli on 09 Feb 2016

24 feb 2016 -- 17:00   [open in google calendar]

Aula Seminari Dipartimento di Matematica di Pisa

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.

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