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arXiv:1406.0519 · Physical Review A

Quantum N -boson states and quantized motion of solitonic droplets: Universal scaling properties in low dimensions

Jeff Maki, Mohammadreza Mohammadi, Fei Zhou

Published Dec 1, 2014• 1 citation
arXivHTMLPDF

Abstract

In this article, we illustrate the scaling properties of a family of solutions for $N$ attractive bosonic atoms in the limit of large $N$. These solutions represent the quantized dynamics of solitonic degrees of freedom in atomic droplets. In dimensions lower than two, or $d=2\ensuremath{-}\ensuremath{\epsilon}$, we demonstrate that the number of isotropic droplet states scales as ${N}^{3/2}/{\ensuremath{\epsilon}}^{1/2}$, and for $\ensuremath{\epsilon}=0$, or $d=2$, scales as ${N}^{2}$. The ground-state energies scale as ${N}^{2/\ensuremath{\epsilon}+1}$ in $d=2\ensuremath{-}\ensuremath{\epsilon}$, and when $d=2$, scale as an exponential function of $N$. We obtain the universal energy spectra and the generalized Tjon relation; their scaling properties are uniquely determined by the asymptotic freedom of quantum bosonic fields at short distances, a distinct feature in low dimensions. We also investigate the effect of quantum loop corrections that arise from various virtual processes and show that the resultant lifetime for a wide range of excited states scales as ${N}^{\ensuremath{\epsilon}/2}{E}^{1\ensuremath{-}\ensuremath{\epsilon}/2}$.

DOI
10.1103/physreva.90.063609

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Using lattice effective field theory, we study the ground state binding energy of NNN distinct particles in two dimensions with equal mass interacting weakly via an attractive SU(N)\mathrm{SU}(N)SU(N)-symmetric short range potential. We find that in the limit of zero range and large NNN, the ratio of binding energies ${B}_{N}∕{B}_{N\ensuremath{-}1}$ approaches the value 8.3(6).