Zero-Range Three-Body Physics in Ultracold Bosonic Gases
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Examensarbete för masterexamen
Programme
Model builders
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Abstract
Due to their universality, effective field theories developed in the study of nuclear
physics have found a direct application in the research of many-body physics in
quantum degenerate gases such as Bose-Einstein condensates. This thesis will reproduce
from one such theory, the zero-range model, the discrete scaling symmetries
emergent for the physical observables of three-body physics in bosonic gases within
the ultracold temperature regime. The conditions of the ultracold regime allow for
the treatment of bosonic gas atoms as quantum-mechanical point particles interacting
exclusively through scattering in the s-wave channel. The Feynman rules
of the zero-range model are derived and implemented to formulate the three-body
scattering amplitude and the three-body bound state equation using the inclusion
of an auxiliary diatomic field operator.
The zero-range model has been shown to be renormalisable within the three-body
sector utilizing a renormalisation group limit cycle through numerical tests of an
ultraviolet cutoff momentum dependent three-body scaling term G(Λ) parametrised
by a three-body parameter Λ∗. The universal properties of the Efimov effect have
been confirmed for the three-body physics of a single species of bosonic gas, as well as
for mixtures of species distinguished by different masses. Furthermore, results for the
three-body scattering amplitude demonstrate the impact of different parameters Λ∗
and two-body scattering lengths on the three-body scattering length of the quantum
degenerate gas.
In conclusion, the zero-range model enables the description of few-body physics of
bosonic quantum degenerate gases with respect to a finite set of parameters: the
masses of gas species, the spin-statistic of gas species, the two-body scattering length
and the three-body parameter, and the temperature of the gas.
Description
Keywords
Bose-Einstein gas, Efimov effect, ultracold, universality, zero-range model