nonrel_fermion Class Reference

Nonrelativistic fermion class. More...

#include <nonrel_fermion.h>

Inheritance diagram for nonrel_fermion:

fermion_T fermion part

Detailed Description

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 pg. 403 or Landau pg. 164.

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

Todo:
Check behaviour of calc_density() at zero density, and compare with that from eff_fermion, rel_fermion, and classical.
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 (for example) to invert the density integral so that we don't need to use a solver.

Definition at line 85 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 pair_mu (const double temper)
 Calculate properties with antiparticles as function of chemical potential.
virtual int pair_density (const double temper)
 Calculate properties with antiparticles 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().

Member Function Documentation

virtual int calc_density ( const double  temper  )  [virtual]

If the density is zero, this function just sets part::mu, part::nu, part::ed, part::pr, and part::en to zero and returns without calling the error handler (even though at zero density and finite temperature, the chemical potentials formally are equal to $ -\infty $).

Implements fermion_T.


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

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