Class fermion_zerot_tl (o2scl)¶
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template<class
fp_t
= double>
classo2scl
::
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.
- 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]
Zero-temperature fermions
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void
kf_from_density
(fermion_tl<fp_t> &f)¶ Calculate the Fermi momentum from the density.
Uses the relation \( k_F = ( 6 \pi^2 n /g )^{1/3} \)
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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
\[ \varepsilon = \frac{g}{2 \pi^2} \int_0^{k_F} k^2 \sqrt{k^2+m^{* 2}} d k \]
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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
\[ P=\frac{g}{6 \pi^2} \int_0^{k_F} \frac{k^4}{\sqrt{k^2+m^{* 2}}} d k \]
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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.
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void
calc_density_zerot
(fermion_tl<fp_t> &f)¶ Zero temperature fermions from o2scl::part_tl::n and o2scl::part_tl::ms.