Abstract We compare effective hyperradial three-body potentials calculated using the S-wave part of the Faddeev equations to calculations using the full Schrödinger equation. As two-body model potential we test both a short-range potential and a Lennard-Jones potential with van der Waals tail. In the former case we find excellent agreement between the two methods for the lowest adiabatic state, indicating that the Faddeev method can be a useful tool also for numerical computations. For excited states the two methods show important differences, but agree for hyperradii larger than about five times the range of the potential (independent of the value of the scattering length and of the number of bound states). For the van der Waals potential, we focus on how well the Faddeev method reproduces the so-called van der Waals universality. We find that indeed the universality is manifest also using this method, but at a slightly different value of the universal parameter κ ∗ . We further derive an efficient method to solve the integro-differential equation arising in the Faddeev method.Abstract We compare effective hyperradial three-body potentials calculated using the S-wave part of the Faddeev equations to calculations using the full Schrödinger equation. As two-body model potential we test both a short-range potential and a Lennard-Jones potential with van der Waals tail. In the former case we find excellent agreement between the two methods for the lowest adiabatic state, indicating that the Faddeev method can be a useful tool also for numerical computations. For excited states the two methods show important differences, but agree for hyperradii larger than about five times the range of the potential (independent of the value of the scattering length and of the number of bound states). For the van der Waals potential, we focus on how well the Faddeev method reproduces the so-called van der Waals universality. We find that indeed the universality is manifest also using this method, but at a slightly different value of the universal parameter κ ∗ . We further derive an efficient method to solve the integro-differential equation arising in the Faddeev method.

Journal of Physics B Atomic Molecular and Optical PhysicsSep 8, 20231 citation

Extending the Adiabatic Theorem

Rachel Berkowitz

PhysicsApr 1, 20260 citations

Two-body correlations in Bose-Einstein condensates

O. Sørensen, D. V. Fedorov, A. S. Jensen +1 more

We formulate a method to study two-body correlations in a condensate of N identical bosons. We use the adiabatic hyperspheric approach and assume a Faddeev-like decomposition of the wave function. We derive for a fixed hyper-radius an integro-differential equation for the angular eigenvalue and wave function. We discuss properties of the solutions and illustrate with numerical results. The correlations lower the interaction energy for $N=20$ by about a factor of 5.We formulate a method to study two-body correlations in a condensate of N identical bosons. We use the adiabatic hyperspheric approach and assume a Faddeev-like decomposition of the wave function. We derive for a fixed hyper-radius an integro-differential equation for the angular eigenvalue and wave function. We discuss properties of the solutions and illustrate with numerical results. The correlations lower the interaction energy for $N=20$ by about a factor of 5.

arXiv:cond-mat/0110069Physical Review AMay 6, 200219 citations

N=20

by about a factor of 5.