Bosons in disc-shaped traps: From 3D to 2D

Autor(en)

K Schnee, Jakob Yngvason

Abstrakt

We present a mathematically rigorous analysis of the ground state of a dilute, interacting Bose gas in a three-dimensional trap that is strongly confining in one direction so that the system becomes effectively two-dimensional. The parameters involved are the particle number, N ≪ 1, the two-dimensional extension, L̄, of the gas cloud in the trap, the thickness, h ≫ L̄ of the trap, and the scattering length a of the interaction potential. Our analysis starts from the full many-body Hamiltonian with an interaction potential that is assumed to be repulsive, radially symmetric and of short range, but otherwise arbitrary. In particular, hard cores are allowed. Under the premises that the confining energy, ∼ 1/h 2, is much larger than the internal energy per particle, and a/h→ 0, we prove that the system can be treated as a gas of two-dimensional bosons with scattering length a 2D = hexp(-(const.)h/a). In the parameter region where a/h ≪ | 1n (ρ̄h 2)| -1, with ρ̄ ∼ N//L̄ 2 the mean density, the system is described by a two-dimensional Gross-Pitaevskii density functional with coupling parameter ∼ Na/h. If | ln(ρ̄h 2)| -1≲ a/h the coupling parameter is ∼ N | ln(ρ̄h 2)| -1 and thus independent of a. In both cases Bose-Einstein condensation in the ground state holds, provided the coupling parameter stays bounded. © 2007 Springer-Verlag.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Erwin Schrödinger Institut

Journal

Communications in Mathematical Physics

Band

269

Seiten

659-691

Anzahl der Seiten

33

ISSN

0010-3616

DOI

https://doi.org/10.1007/s00220-006-0136-8

Publikationsdatum

2007

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/bf4f9935-3171-4313-82e0-1a4fc0532b81