Quantum N-Boson States and Quantized Motion of Solitonic Droplets: Universal Scaling Properties in Low Dimensions

الأصل · EN

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-ε, we demonstrate that the number of isotropic droplet states scales as N³/²/ε¹/², and for ε=0, or d=2, scales as N². The ground state energies scale as N² / ε⁺ ¹ in d=2-ε, 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 Nε/²E¹⁻ε/².