Energies

Kinetic Energy

tdg.observable.energy.Kinetic(ensemble)

The total kinetic energy,

\[\left\langle \texttt{Kinetic} \right\rangle = \left\langle \sum_{ab\sigma} \tilde{\psi}^{\dagger}_{a\sigma} \tilde{\kappa}_{ab} \tilde{\psi}_{b\sigma} \right\rangle,\]

one per configuration.

tdg.observable.energy.kinetic_by_kF4(ensemble)

The baryon mass times the kinetic energy density normalized by the Fermi momentum.

\[\frac{k}{k_F^4} = \frac{MK}{k_F^4 L^2} = \frac{KML^2}{(k_F L)^4} = \frac{\texttt{Kinetic}}{(2\pi \texttt{N})^2}\]

Potential Energy

tdg.observable.energy.Potential(ensemble)

The total potential energy,

\[\left\langle \texttt{Potential} \right\rangle = \left\langle \frac{1}{2} \sum_{ab} \tilde{n}_a \tilde{V}_{ab} \tilde{n}_b - \frac{N_x^2 C_0}{2} \sum_a \tilde{n}_a \right\rangle,\]

one per configuration.

tdg.observable.energy.potential_by_kF4(ensemble)

The baryon mass times potential energy density normalized by the Fermi momentum.

\[\frac{v}{k_F^4} = \frac{MV}{k_F^4 L^2} = \frac{VML^2}{(k_F L)^4} = \frac{\texttt{Potential}}{(2\pi \texttt{N})^2}\]

Internal Energy

tdg.observable.energy.InternalEnergy(ensemble)

The total internal energy,

\[\left\langle \texttt{InternalEnergy} \right\rangle = \left\langle \tilde{K} + \tilde{V} - \tilde{\mu} \tilde{N} - \tilde{h}\cdot \tilde{S} \right\rangle\]

one per configuration.

tdg.observable.energy.internalEnergy_by_kF4(ensemble)

The baryon mass times the internal energy density normalized by the Fermi momentum.

\[\frac{u}{k_F^4} = \frac{MU}{k_F^4 L^2} = \frac{UML^2}{(k_F L)^4} = \frac{\texttt{InternalEnergy}}{(2\pi \texttt{N})^2}\]