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A Hyperspherical Treatment of the N-Fermion problem.

Seth T. Ritenhouse, Javier von Stecher, Chris H. Greene +1 more

Bulletin of the American Physical SocietyMay 19, 20060 citations

Collective Coordinate Description of Anisotropically Trapped Degenerate Fermi Gases

Seth T. Rittenhouse, M. J. Cavagnero, Chris H. Greene

The solution of the many-body Schrödinger equation using an adiabatic treatment of the hyperradius is generalized to treat two components of a hyperspherical vector adiabatically. This treatment has advantages in certain physical situations, such as the description of a degenerate Fermi gas or Bose-Einstein condensate in an anisotropic trapping potential. A first application to the zero-temperature anisotropic Fermi gas is compared with predictions of the Hartree-Fock method.

The Journal of Physical Chemistry ANov 10, 20092 citations

Renormalized contact interaction in degenerate unitary Bose gases

Yijue Ding, Chris H. Greene

We renormalize the two-body contact interaction based on the exact solution of two interacting particles in a harmonic trap. This renormalization extends the validity of the contact interaction to large scattering lengths. We apply this renormalized interaction to a degenerate unitary Bose gas to study its stationary properties and elementary excitations using the mean-field theory and the hyperspherical method. Since the scattering length is no longer a relevant length scale at unitarity, universal properties are obtained that depend only on the average particle density. Our treatment shows that the universal relations for the total energy and for the two-body contact are $E/N=12.67{\ensuremath{\hbar}}^{2}\ensuremath{\langle}{n}^{2/3}\ensuremath{\rangle}/2m$ and ${C}_{2}/N=11.8\ensuremath{\langle}{n}^{1/3}\ensuremath{\rangle}$, respectively.We renormalize the two-body contact interaction based on the exact solution of two interacting particles in a harmonic trap. This renormalization extends the validity of the contact interaction to large scattering lengths. We apply this renormalized interaction to a degenerate unitary Bose gas to study its stationary properties and elementary excitations using the mean-field theory and the hyperspherical method. Since the scattering length is no longer a relevant length scale at unitarity, universal properties are obtained that depend only on the average particle density. Our treatment shows that the universal relations for the total energy and for the two-body contact are $E/N=12.67{\ensuremath{\hbar}}^{2}\ensuremath{\langle}{n}^{2/3}\ensuremath{\rangle}/2m$ and ${C}_{2}/N=11.8\ensuremath{\langle}{n}^{1/3}\ensuremath{\rangle}$, respectively.

arXiv:1701.03912Physical Review AMay 2, 201714 citations

Collapse of a degenerate Fermi gas

Robert J. Brecha, Giovanni Carlo Modugno, G. Roati +3 more

APSOct 1, 20020 citations

A Hyperspherical Variational Approach to the N-Fermion Problem

Seth T. Rittenhouse, M. J. Cavagnero, J. von Stecher +1 more

Few-Body SystemsApr 27, 20062 citations

The degenerate Fermi gas with renormalized density-dependent interactions in the K harmonic approximation

Seth T. Rittenhouse, Chris H. Greene

We present a simple implementation of a density-dependent, zero-range interactions in a degenerate Fermi gas described in hyperspherical coordinates. The method produces a 1D effective potential which accurately describes the ground state energy as a function of the hyperradius, the rms radius of the two spin component gas throughout the unitarity regime. In the unitarity regime the breathing mode frequency is found to limit to the non-interacting value. A dynamical instability, similar to the Bosenova, is predicted to be possible in gases containing more than three spin components, for large, negative, two-body scattering lengths.We present a simple implementation of a density-dependent, zero-range interactions in a degenerate Fermi gas described in hyperspherical coordinates. The method produces a 1D effective potential which accurately describes the ground state energy as a function of the hyperradius, the rms radius of the two spin component gas throughout the unitarity regime. In the unitarity regime the breathing mode frequency is found to limit to the non-interacting value. A dynamical instability, similar to the Bosenova, is predicted to be possible in gases containing more than three spin components, for large, negative, two-body scattering lengths.

arXiv:physics/0702161Feb 20, 20070 citations

Describing the degenerate Fermi in a renormalized hyperspherical treatment

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Describing the degenerate Fermi in a renormalized hyperspherical treatment

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