We consider $N$ bosons in two dimensions, interacting through a potential whose scattegin length is exponentially small in the number of particles of the systems (Gross-Pitaevskii regime). For this system we provide an expression for the ground state energy and the low energy excitation spectrum of $N$, up to errors vanishing with $N$. Our result represents the first case where the validity of Bogoliubov predictions for the low energy spectrum of a dilute two dimensional Bose gas has been established in a scaling where the dimensionality of the system plays a role.

The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime

Serena Cenatiempo
Membro del Collaboration Group
;
2023-01-01

Abstract

We consider $N$ bosons in two dimensions, interacting through a potential whose scattegin length is exponentially small in the number of particles of the systems (Gross-Pitaevskii regime). For this system we provide an expression for the ground state energy and the low energy excitation spectrum of $N$, up to errors vanishing with $N$. Our result represents the first case where the validity of Bogoliubov predictions for the low energy spectrum of a dilute two dimensional Bose gas has been established in a scaling where the dimensionality of the system plays a role.
2023
two dimensional bosons
Gross-Pitaevekii regime
Bogoliubov theory
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/24906
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