nonrel_fermion Class Reference

#include <nonrel_fermion.h>

Inheritance diagram for nonrel_fermion:

fermion part

Detailed Description

Nonrelativistic fermion class.

The rest mass energy density is given by n*m not n*ms. Note that the effective mass here is the Landau mass, not the Dirac mass.

Pressure is computed with

\[ P = 2 \varepsilon/3 \]

and entropy density with

\[ s = \frac{5 \varepsilon}{3 T} - \frac{n \mu}{T} \]

These relations can be verified with an integration by parts. See, e.g. Callen's "Thermodynamics and an introduction to thermostatistics", 2nd edition, pg. 403 or Landau and Lifshitz, Stat. Phys. 3rd edition, part 1, pg. 164.

Note that the energy density integral can be rescaled:

\[ \varepsilon = \frac{T^{5/2}(2 m^{*})^{3/2}}{\pi^2} \int_0^{\infty} d u \frac{u^{3/2}}{1 + \exp(u-y)} \]

where $ u = k^2/2/m^{*}/T $ and $ y=\mu/T $.

The functions fermion::pair_density() and pair_mu() have not been implemented.

Todo:
I think calc_mu_zerot() and calc_density_zerot() are missing the proper dependence on the degeneracy, g. (8/20/07) (I think this is fixed now, but should be tested, 8/22/07)
Todo:
Make sure to test with non-interacting equal to true or false, and document whether or not it works with both inc_rest_mass equal to true or false
Idea for future:
This could be improved by performing a Chebyshev approximation to invert the density integral so that we don't need to use a solver.

Definition at line 82 of file nonrel_fermion.h.


Public Member Functions

 nonrel_fermion (double m=0.0, double g=0.0)
 Create a nonrelativistic fermion with mass 'm' and degeneracy 'g'.
virtual int calc_mu_zerot ()
 Zero temperature fermions.
virtual int calc_density_zerot ()
 Zero temperature fermions.
virtual int calc_mu (const double temper)
 Calculate properties as function of chemical potential.
virtual int calc_density (const double temper)
 Calculate properties as function of density.
virtual int nu_from_n (const double temper)
 Calculate effective chemical potential from density.
int set_density_root (root< double, funct< double > > &rp)
 Set the solver for use in calculating the chemical potential from the density.
virtual const char * type ()
 Return string denoting type ("nonrel_fermion").

Data Fields

cern_mroot_root< double, funct
< double > > 
def_density_root
 The default solver for calc_density().

The documentation for this class was generated from the following file:

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