// Calculate U_{1}/N = 1/N \sum_k \epsilon_h(k) f_h(\xi_h(k))
func HolonEnergy(env *tempAll.Environment) (float64, error) {
inner := func(k vec.Vector) float64 {
return env.Epsilon_h(k) * env.Fermi(env.Xi_h(k))
}
dim := 2
avg := bzone.Avg(env.PointsPerSide, dim, inner)
return avg, nil
}
// Return the absolute error and gradient for the doping w.r.t. the given
// parameters.
func AbsErrorMu_h(env *tempAll.Environment, variables []string) solve.Diffable {
F := func(v vec.Vector) (float64, error) {
env.Set(v, variables)
L := env.PointsPerSide
lhs := 2.0 / (env.T0 + env.Tz)
rhs := bzone.Avg(L, 2, tempAll.WrapFunc(env, innerMu_h))
return lhs - rhs, nil
}
h := 1e-5
epsabs := 1e-4
return solve.SimpleDiffable(F, len(variables), h, epsabs)
}
func AbsErrorMu_h(env *tempAll.Environment, variables []string) solve.Diffable {
F := func(v vec.Vector) (float64, error) {
env.Set(v, variables)
if -env.Mu_b > -2.0*env.Mu_h {
// when |Mu_b| is this large, no longer have pairs
return env.X - tempPair.X1(env), nil
}
L := env.PointsPerSide
lhs := 0.5 / (env.T0 + env.Tz)
rhs := bzone.Avg(L, 2, tempAll.WrapFunc(env, innerMu_h))
return lhs - rhs, nil
}
h := 1e-5
epsabs := 1e-4
return solve.SimpleDiffable(F, len(variables), h, epsabs)
}
// Concentration of unpaired holons
func X1(env *tempAll.Environment) float64 {
L := env.PointsPerSide
return bzone.Avg(L, 2, tempAll.WrapFunc(env, innerX1))
}