Class fermion_zerot_tl (o2scl)

O2scl_part : Class List

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

Fermion properties at zero temperature.

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.

Todo

In class fermion_zerot_tl:

  • 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]

Zero-temperature fermions

inline void kf_from_density(fermion_tl<fp_t> &f)

Calculate the Fermi momentum from the density.

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

inline void energy_density_zerot(fermion_tl<fp_t> &f)

Energy density at T=0 from o2scl::fermion_tl::kf and o2scl::part_tl::ms.

Calculates the integral

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

inline void pressure_zerot(fermion_tl<fp_t> &f)

Pressure at T=0 from o2scl::fermion_tl::kf and o2scl::part_tl::ms.

Calculates the integral

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

inline 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.

inline virtual void calc_density_zerot(fermion_tl<fp_t> &f)

Zero temperature fermions from o2scl::part_tl::n and o2scl::part_tl::ms.

Public Functions

inline fermion_zerot_tl()
inline virtual ~fermion_zerot_tl()

Protected Attributes

fp_t pi

Store \( \pi \) for convenience.

fp_t pi2

Store \( \pi^2 \) for convenience.