Deformation Dependence of Breathing Oscillations in Bose - Fermi Mixtures at Zero Temperature
2014
We study the breathing
oscillationsin bose-fermi mixtures in the axially-symmetric deformed trap of
prolate, spherical and
oblateshapes, and clarify the def ormation dependence of the frequencies and the characteristics of collective
oscillations. The co llective
oscillationsof the mixtures in deformed traps are calculated in the scaling method. In largely-deformed
prolateand
oblatelimits and spherical limit, we obtain the analytical expressions of th e collective frequencies. The full calculation shows that the collective
oscillationsbecome consistent with the analytically-obtained frequencies when the system is deformed into both
prolateand
oblateregions. The complicated changes of
oscillationcharacters are shown to occur in the
transcendentalr egions around the spherically-deformed region. We find that these critical changes of
oscillationch aracters are explained by the
level crossingbehaviors of the intrinsic
oscillationmodes. The approximate expressions are obtained for the
level crossingpoints that determine the
transcendentalregions. We also compare the results of the scaling methods with those of the dynamical approach.
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