Energetics of three interacting mass-imbalanced bodies in a three-dimensional spherical harmonic trap
arxiv(2022)
摘要
We consider a system of three particles, either three identical bosons or two
identical fermions plus an impurity, within a three-dimensional isotropic trap
interacting via a contact interaction. Using two approaches, one using an
infinite sum of basis states for the wavefunction and the other a closed form
wavefunction, we calculate the allowable energy eigenstates of the system as a
function of the interaction strength, including the strongly and weakly
interacting limits. For the fermionic case this is done while maintaining
generality regarding particle masses. We find that the two methods of
calculating the spectrum are in excellent agreement in the strongly interacting
limit. However the infinite sum approach is unable to uniquely specify the
energy of Efimov states, but in the strongly interacting limit there is, to a
high degree of accuracy, a correspondence between the three-body parameter
required by the boundary condition of the closed form approach and the
summation truncation order required by the summation approach. This
specification of the energies and wavefunctions forms the basis with which
thermodynamic variables such as the virial coefficients or Tan contacts, or
dynamic phenomena like quench dynamics can be calculated.
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