Structure of the excitation spectrum for many-body quantum systems

Seiringer R. 2014. Structure of the excitation spectrum for many-body quantum systems. Proceeding of the International Congress of Mathematicans. ICM: International Congress of Mathematicans vol. 3, 1175–1194.

Conference Paper | Published | English

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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.
Publishing Year
Date Published
2014-08-01
Proceedings Title
Proceeding of the International Congress of Mathematicans
Volume
3
Page
1175-1194
Conference
ICM: International Congress of Mathematicans
Conference Location
Seoul, South Korea
Conference Date
2014-08-13 – 2014-08-21
IST-REx-ID

Cite this

Seiringer R. Structure of the excitation spectrum for many-body quantum systems. In: Proceeding of the International Congress of Mathematicans. Vol 3. Kyung Moon SA; 2014:1175-1194.
Seiringer, R. (2014). Structure of the excitation spectrum for many-body quantum systems. In Proceeding of the International Congress of Mathematicans (Vol. 3, pp. 1175–1194). Seoul, South Korea: Kyung Moon SA.
Seiringer, Robert. “Structure of the Excitation Spectrum for Many-Body Quantum Systems.” In Proceeding of the International Congress of Mathematicans, 3:1175–94. Kyung Moon SA, 2014.
R. Seiringer, “Structure of the excitation spectrum for many-body quantum systems,” in Proceeding of the International Congress of Mathematicans, Seoul, South Korea, 2014, vol. 3, pp. 1175–1194.
Seiringer R. 2014. Structure of the excitation spectrum for many-body quantum systems. Proceeding of the International Congress of Mathematicans. ICM: International Congress of Mathematicans vol. 3, 1175–1194.
Seiringer, Robert. “Structure of the Excitation Spectrum for Many-Body Quantum Systems.” Proceeding of the International Congress of Mathematicans, vol. 3, Kyung Moon SA, 2014, pp. 1175–94.
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