The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas

Details The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas

2007-07-15

arxiv.org/abs/0707.2196v1

Phys. Rev. A 76, 043609 (2007)

Physics

Condensed Matter

Other Condensed Matter

9 pages, 8 figures

Scientific paper

10.1103/PhysRevA.76.043609

We study the reduced single-particle density matrix (RSPDM), the momentum distribution, natural orbitals and their occupancies, of dark "soliton" (DS) states in a Tonks-Girardeau gas. DS states are specially tailored excited many-body eigenstates, which have a dark solitonic notch in their single-particle density. The momentum distribution of DS states has a characteristic shape with two sharp spikes. We find that the two spikes arise due to the high degree of correlation observed within the RSPDM between the mirror points ($x$ and $-x$) with respect to the dark notch at $x=0$; the correlations oscillate rather than decay as the points $x$ and $-x$ are being separated.

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