Protected Attributes | List of all members
o2scl::fermion_zerot_tl< fp_t > Class Template Reference

Fermion properties at zero temperature. More...

#include <fermion.h>

Detailed Description

template<class fp_t = double>
class o2scl::fermion_zerot_tl< fp_t >

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_thermo_tl 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 131 of file fermion.h.

Public Member Functions

Zero-temperature fermions
void kf_from_density (fermion_tl< fp_t > &f)
 Calculate the Fermi momentum from the density. More...
 
void energy_density_zerot (fermion_tl< fp_t > &f)
 Energy density at T=0 from o2scl::fermion_tl::kf and o2scl::part_tl::ms. More...
 
void pressure_zerot (fermion_tl< fp_t > &f)
 Pressure at T=0 from o2scl::fermion_tl::kf and o2scl::part_tl::ms. More...
 
virtual void calc_mu_zerot (fermion_tl< fp_t > &f)
 Zero temperature fermions from o2scl::part_tl::mu or o2scl::part_tl::nu and o2scl::part_tl::ms.
 
virtual void calc_density_zerot (fermion_tl< fp_t > &f)
 Zero temperature fermions from o2scl::part_tl::n and o2scl::part_tl::ms. More...
 

Protected Attributes

fp_t pi
 Desc.
 
fp_t pi2
 Desc.
 

Member Function Documentation

◆ calc_density_zerot()

template<class fp_t = double>
virtual void o2scl::fermion_zerot_tl< fp_t >::calc_density_zerot ( fermion_tl< fp_t > &  f)
inlinevirtual

Reimplemented in o2scl::fermion_nonrel_tl< inte_t, fp_t >.

Definition at line 255 of file fermion.h.

◆ energy_density_zerot()

template<class fp_t = double>
void o2scl::fermion_zerot_tl< fp_t >::energy_density_zerot ( fermion_tl< fp_t > &  f)
inline

Calculates the integral

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

Definition at line 171 of file fermion.h.

◆ kf_from_density()

template<class fp_t = double>
void o2scl::fermion_zerot_tl< fp_t >::kf_from_density ( fermion_tl< fp_t > &  f)
inline

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

Definition at line 157 of file fermion.h.

◆ pressure_zerot()

template<class fp_t = double>
void o2scl::fermion_zerot_tl< fp_t >::pressure_zerot ( fermion_tl< fp_t > &  f)
inline

Calculates the integral

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

Definition at line 196 of file fermion.h.


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

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