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Register a new userDynamics of one-dimensional quantum droplets
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Added by
Grigori E. Astrakharchik
Publication date
2018
fields
Physics
and research's language is
English
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The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large `puddles with a broad flat-top plateau. Small droplets collide quasi-elastically, featuring the soliton-like behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.
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We study the statistical mechanics and the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets described by a modified Gross-Pitaevskii equation. To determine the classical partition function thereof, we leverage the semi-analytical transfer integral operator (TIO) technique. The latter predicts a distribution of the observed wave function amplitudes and yields two-point correlation functions providing insights into the emergent dynamics involving quantum droplets. We compare the ensuing TIO results with the probability distributions obtained at large times of the modulationally unstable dynamics as well as with the equilibrium properties of a suitably constructed Langevin dynamics. We find that the instability leads to the spontaneous formation of quantum droplets featuring multiple collisions and consecutively are found to coalesce at large evolution times. Our results from the distinct methodologies are in good agreement aside from the case of low temperatures in the special limit where the droplet widens. In this limit, the distribution acquires a pronounced bimodal character, exhibiting a deviation between the TIO solution and the Langevin dynamics still captured by the modified Gross-Pitaevskii framework.
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