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README.md

Noninteracting fermions in the canonical ensemble

This project contains several codes for calculating thermodynamic properties of noninteracting fermions in the canonical ensemble (of fixed numbers of particles) and the grand-canonical ensemble, in arbitrary dimensions.

The code currently is written for isotropic harmonic trapping potentials, but can easily be changed to support other geometries.

The main file is free_fermi.f90, which contains routines for calculating:

  • The partition function Z
  • The free energy F = E - T S = -T log(Z)
  • The thermal energy E
  • The heat capacity C
  • The single-particle occupations n(k)

It has been tested by doing the calculations in two ways. First, free_fermi.f90 uses particle-number projection (via a Fourier transform) to calculate canonical-ensemble quantities. Second, an alternate code (in the altsrc directory) uses arbitrary precision arithmetic and a set for recursive formulas based on the paper J. Chem. Phys. 98, 2484 (1993). The two codes give identical results.

Finally, free_fermi_gc.f90 contains some simple routines for calculating thermodynamic quantities in the grand-canonical ensemble. (They are not as robust or as extensive as the canonical routines.)

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Noninteracting fermions in a harmonic trap

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