Rapidly rotating BoseEinstein condensates in strongly anharmonic traps
Abstract
We study a rotating BoseEinstein condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of twodimensional GrossPitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1/{epsilon}{sup 2} and we are interested in the limit {epsilon}{yields}0 (ThomasFermi limit) with the angular velocity {omega} depending on {epsilon}. We derive rigorously the leading asymptotics of the ground state energy and the density profile when {omega} tends to infinity as a power of 1/{epsilon}. If {omega}({epsilon})={omega}{sub 0}/{epsilon} a ''hole'' (i.e., a region where the density becomes exponentially small as 1/{epsilon}{yields}{infinity}) develops for {omega}{sub 0} above a certain critical value. If {omega}({epsilon})>>1/{epsilon} the hole essentially exhausts the container and a ''giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const vertical bar log {epsilon} vertical bar <{omega}({epsilon}) < or approx. const/{epsilon}.
 Authors:
 Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna (Austria)
 (Austria)
 (Austria) and Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna (Austria)
 Publication Date:
 OSTI Identifier:
 20929681
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 4; Other Information: DOI: 10.1063/1.2712421; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR VELOCITY; BOSEEINSTEIN CONDENSATION; BOUNDARYVALUE PROBLEMS; COUPLING CONSTANTS; GROUND STATES; SYMMETRY BREAKING; THIN FILMS; THOMASFERMI MODEL; TRAPS; TWODIMENSIONAL CALCULATIONS
Citation Formats
Correggi, M., RindlerDaller, T., Yngvason, J., Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna, and Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna. Rapidly rotating BoseEinstein condensates in strongly anharmonic traps. United States: N. p., 2007.
Web. doi:10.1063/1.2712421.
Correggi, M., RindlerDaller, T., Yngvason, J., Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna, & Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna. Rapidly rotating BoseEinstein condensates in strongly anharmonic traps. United States. doi:10.1063/1.2712421.
Correggi, M., RindlerDaller, T., Yngvason, J., Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna, and Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna. Sun .
"Rapidly rotating BoseEinstein condensates in strongly anharmonic traps". United States.
doi:10.1063/1.2712421.
@article{osti_20929681,
title = {Rapidly rotating BoseEinstein condensates in strongly anharmonic traps},
author = {Correggi, M. and RindlerDaller, T. and Yngvason, J. and Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna and Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna},
abstractNote = {We study a rotating BoseEinstein condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of twodimensional GrossPitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1/{epsilon}{sup 2} and we are interested in the limit {epsilon}{yields}0 (ThomasFermi limit) with the angular velocity {omega} depending on {epsilon}. We derive rigorously the leading asymptotics of the ground state energy and the density profile when {omega} tends to infinity as a power of 1/{epsilon}. If {omega}({epsilon})={omega}{sub 0}/{epsilon} a ''hole'' (i.e., a region where the density becomes exponentially small as 1/{epsilon}{yields}{infinity}) develops for {omega}{sub 0} above a certain critical value. If {omega}({epsilon})>>1/{epsilon} the hole essentially exhausts the container and a ''giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const vertical bar log {epsilon} vertical bar <{omega}({epsilon}) < or approx. const/{epsilon}.},
doi = {10.1063/1.2712421},
journal = {Journal of Mathematical Physics},
number = 4,
volume = 48,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}

We extend the results of a previous paper on the GrossPitaevskii description of rotating BoseEinstein condensates in twodimensional traps to confining potentials of the form V(r)=r{sup s}, 2<s<{infinity}. Writing the coupling constant as 1/{epsilon}{sup 2}, we study the limit {epsilon}{yields}0. We derive rigorously the leading asymptotics of the ground state energy and the density profile when the rotation velocity {omega} tends to infinity as a power of 1/{epsilon}. The case of asymptotically homogeneous potentials is also discussed.

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