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o2scl::fermion_zerot Class Reference

Fermion properties at zero temperature. More...

#include <fermion.h>

Inheritance diagram for o2scl::fermion_zerot:
o2scl::fermion_eval_thermo o2scl::fermion_mag_zerot o2scl::fermion_eff o2scl::fermion_nonrel o2scl::fermion_rel

Public Member Functions

Zero-temperature fermions
void kf_from_density (fermion &f)
 Calculate the Fermi momentum from the density. More...
void energy_density_zerot (fermion &f)
 Energy density at T=0 from fermion::kf and part::ms. More...
void pressure_zerot (fermion &f)
 Pressure at T=0 from fermion::kf and part::ms. More...
virtual void calc_mu_zerot (fermion &f)
 Zero temperature fermions from part::mu or part::nu and part::ms.
virtual void calc_density_zerot (fermion &f)
 Zero temperature fermions from part::n and part::ms.

Detailed Description

This is a base class for the computation of fermionic statistics at zero temperature. The more general case of finite temperature is taken care of by fermion_eval_thermo objects. The primary functions are calc_mu_zerot() and calc_density_zerot() which compute all the thermodynamic quantities as a function of the chemical potential, or the density, respectively.

Idea for Future:
Use hypot() and other more accurate functions for the analytic expressions for the zero temperature integrals. [Progress has been made, but there are probably other functions which may break down for small but finite masses and temperatures]

Definition at line 123 of file fermion.h.

Member Function Documentation

◆ energy_density_zerot()

void o2scl::fermion_zerot::energy_density_zerot ( fermion f)

Calculates the integral

\[ \varepsilon = \frac{g}{2 \pi^2} \int_0^{k_F} k^2 \sqrt{k^2+m^{* 2}} d k \]

◆ kf_from_density()

void o2scl::fermion_zerot::kf_from_density ( fermion f)

Uses the relation $ k_F = ( 6 \pi^2 n /g )^{1/3} $

◆ pressure_zerot()

void o2scl::fermion_zerot::pressure_zerot ( fermion f)

Calculates the integral

\[ P=\frac{g}{6 \pi^2} \int_0^{k_F} \frac{k^4}{\sqrt{k^2+m^{* 2}}} d k \]

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

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