# Effect of Gravitation on Noninteracting Trapped Fermions

## TBMG-3077

## 03/01/2002

- Content
A report presents a theoretical study of the thermodynamics of an ultralow-temperature gas of fermions that interact with a gravitational field and with an externally imposed trapping potential but not with each other. The gravitational field is taken to define the z axis and the trapping potential to be of the form (m/2) (ωxx2+ωyy2+ωzz2), where m is the mass of a fermion; x, y, and z are Cartesian coordinates originating at the center of the trap; and the ω values denote effective harmonic- oscillator angular frequencies with respect to motion along the respective coordinate axes. The single-particle energy is found from the solution of the time-dependent Schroedinger equation for a Hamiltonian that includes kinetic energy plus the gravitational and trapping potentials. The equation for the single-particle energy is combined with Fermi statistics to obtain equations for the chemical potential, internal energy, and specific heat of the gas; the number of trapped fermions; and the spatial distribution of fermions at zero temperature. The equations reveal the ways in which the Fermi energy, the specific heat, and the shape of the Fermion cloud are affected by the gravitational field and the anisotropy of the trapping field.

- Citation
- "Effect of Gravitation on Noninteracting Trapped Fermions," Mobility Engineering, March 1, 2002.