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arXiv · 0707.2196

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

H. Buljan·K. Lelas·R. Pezer·M. Jablan
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Abstract

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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H. Buljan, K. Lelas, R. Pezer, M. Jablan. 2007-07-15. The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas. https://doi.org/10.1103/physreva.76.043609

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