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arXiv:2609.17097

Course on two-dimensional quantum gases

Hélène Perrin

cond-mat.quant-gasphysics.atom-phquant-phSubmitted Sep 15, 2026• Announced Sep 16, 2026• 0 citations

Abstract

This course on two-dimensional quantum gases, prepared for the S{ã}o Paulo ICTP-SAIFR IVth School on Light and Cold Atoms, is organized into three lectures. The first introductory lecture addresses Bose-Einstein condensation in an ideal gas, the effect of interactions in the weakly interacting limit, Gross-Pitaevskii equation and its hydrodynamic formulation, as well as superfluidity. The second lecture is devoted to the main features of two-dimensional quantum gases: importance of the interactions, enhanced phase fluctuations and the emergence of a quasi long-range order, superfluidity through the Berezinskii-Kosterlitz-Thouless mechanism, scaling symmetry. The third lecture has taken the form of a seminar on fast rotating quasi two-dimensional Bose gases and thermal melting of the vortex lattice. The slides accompanying these notes can be found on the school website: https://www.ictp-saifr.org/slca2025/.

Journal reference: Sao Paulo ICTP-SAIFR IVth School on Light and Cold Atoms, Oct 2025, S{ã}o Paulo, Brazil
Comments: 67 pages. Comments welcome

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The material presented here consists of lecture notes written for a five two-hour sections course given during the 2004 edition of the Brazilian School on Statistical Mechanics.The topics covered are 1.Bose-Einstein condensation of trapped ideal gases; 2. Effective two-body interactions and exact results in the Gross-Pitaevski limit; 3. Atomic structure effects, including "Feshbach resonances" and hybrid condensates; 4. Elementary excitations in the Bogoliubov approximation and beyond; and 5. Splitt traps, interference phenomena and condensate arrays.

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