Abstract
The ground state of a Bose-Einstein condensate in a two-dimensional trap potential is analyzed numerically at the infinite-particle limit. It is shown that the anisotropy of the many-particle position variance along the x and y axes can be opposite when computed at the many-body and mean-field levels of theory. This is despite the system being 100% condensed, and the respective energies per particle and densities per particle to coincide.
Highlights
We consider the ground state of N interacting bosons in a two-dimensional trap. It has been shown under quite general conditions [1, 2, 3] that the many-body energy per particle and density per particle coincide at the infinite-particle limit with the Gross-Pitaevskii mean-field results, lim ρ(r) N
The infinite-particle limit implies that the interaction parameter, i.e., the product of the number of particles times the interaction strength, is kept fixed when N → ∞
It has not been shown that the ground state can exhibit opposite anisotropy of the variance at the infinite-particle limit, i.e., that the many-body and mean-field anisotropies of 100% condensed bosons are different. This is the main finding of the present work, i.e., that trapped Bose-Einstein condensates at the infinite-particle limit can be classified according to whether the anisotropies of their many-body and mean-field position variances are alike or opposite
Summary
We consider the ground state of N interacting bosons in a two-dimensional trap. It has been shown under quite general conditions [1, 2, 3] that the many-body energy per particle and density per particle coincide at the infinite-particle limit with the Gross-Pitaevskii mean-field results, lim N →∞ ρ(r) N =|φGP (r)|2, lim E N→∞ N = εGP . (1)Here, the density is the diagonal of the reduced one-particle density matrix [4, 5], ρ(r) ≡ ρ(1)(r, r), E is the ground-state energy, φGP (r) and εGP are the Gross-Pitaevskii orbital and energy, respectively, and r = (x, y). The question arises, which differences are there, at the infinite-particle limit, between the many-body and mean-field descriptions of trapped bosons in their ground state.
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