Orthogonality Catastrophe in Bose-Einstein Condensates

Details Orthogonality Catastrophe in Bose-Einstein Condensates Orthogonality Catastrophe in Bose-Einstein Condensates

2004-04-26

arxiv.org/abs/cond-mat/0404590v3

Physics

Condensed Matter

Statistical Mechanics

5 pages; 2 figures

Scientific paper

Orthogonality catastrophe in fermionic systems is well known: in the thermodynamic limit, the overlap between the ground state wavefunctions with and without a single local scattering potential approaches zero algebraically as a function of the particle number $N$. Here we examine the analogous problem for bosonic systems. In the homogeneous case, we find that ideal bosons display an orthogonality stronger than algebraic: the wavefunction overlap behaves as ${\rm exp}[-\lambda N^{1/3}]$ in three dimensions and as ${\rm exp}[-\lambda N/\ln ^2 N]$ in two dimensions. With interactions, the overlap becomes finite but is still (stretched-)exponentially small for weak interactions. We also consider the cases with a harmonic trap, reaching similar (though not identical) conclusions. Finally, we comment on the implications of our results for spectroscopic experiments and for (de)coherence phenomena.

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