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Tied and bound

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Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases.

For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered.

Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. To reach the universal Efimov regime in which the size of the Tied and bound trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.

Energy of the four-body excited state supported by model I at unitarity.

Characteristics of model III at unitarity. Energies of the excited four-body states at unitarity. The horizontal dashed line in panel b shows the corresponding energy ratio for model II.

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The energies and scattering lengths are scaled by the short-range quantities E sr and r BXrespectively the energy is shown on a square-root Tied and bound. The solid line shows the energy E 3 exc1 of the BBX system.

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The circles and squares show the real part E r of the resonance energies of the BBBX system to guide the eye, the dotted line connects consecutive points for the energetically lower-lying resonance. The symbols show the four-body energies E 4 as a function of the inverse of the number N b of basis functions.

The displayed energies correspond to the 8th through 14th eigenvalue of the generalized eigenvalue problem.

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However, the complex scaling did not reveal such a resonance. This is likely due to the fact that the energetically higher-lying plateau is not a signature of a resonance but related to a BBX bound state. For vanishing rotation angle, the imaginary part of the energy is zero. This figure and Fig.

Few-boson system with a single impurity: Universal bound states tied to Efimov trimers D. A 99— Published 16 January Abstract Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases.


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