Physics – Mathematical Physics
Scientific paper
2005-10-01
Physics
Mathematical Physics
Corrected version. To be published in Communications in Mathematical Physics
Scientific paper
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, $N\gg 1$, the two-dimensional extension, $\bar L$, of the gas cloud in the trap, the thickness, $h\ll \bar L$ 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 premisses that the confining energy, $\sim 1/h^2$, is much larger than the internal energy per particle, and $a/h\to 0$, we prove that the system can be treated as a gas of two-dimensional bosons with scattering length $a_{\rm 2D}= h\exp(-(\hbox{\rm const.)}h/a)$. In the parameter region where $a/h\ll |\ln(\bar\rho h^2)|^{-1}$, with $\bar\rho\sim N/\bar L^2$ the mean density, the system is described by a two-dimensional Gross-Pitaevskii density functional with coupling parameter $\sim Na/h$. If $|\ln(\bar\rho h^2)|^{-1}\lesssim a/h$ the coupling parameter is $\sim N |\ln(\bar\rho h^2)|^{-1}$ and thus independent of $a$. In both cases Bose-Einstein condensation in the ground state holds, provided the coupling parameter stays bounded.
Schnee K.
Yngvason Jakob
No associations
LandOfFree
Bosons in Disc-Shaped Traps: From 3D to 2D does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bosons in Disc-Shaped Traps: From 3D to 2D, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bosons in Disc-Shaped Traps: From 3D to 2D will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-612140