func innerMu_h(env *tempAll.Environment, k vec.Vector) float64 {
sxy := math.Sin(k[0]) - math.Sin(k[1])
numer := sxy * sxy * math.Tanh(env.Beta*env.Xi_h(k)/2.0)
denom := env.Mu_b + 2.0*env.Xi_h(k)
//denom := env.Mu_b - 2.0*env.Be_field*env.A + 2.0*env.Xi_h(k)
return numer / denom
}
func innerMu_h(env *tempAll.Environment, k vec.Vector) float64 {
sxy := math.Sin(k[0]) - math.Sin(k[1])
E := env.BogoEnergy(k)
xi := env.Xi_h(k)
delta := env.Delta_h(k)
return sxy * sxy * math.Tanh(env.Beta*E/2.0) * (2.0*xi*xi + delta*delta) / (E * E * E)
}
// 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
}
// Evaluate the retarded pair Green's function Pi_R(k, omega)_{xx, xy, yy}.
// k must be a two-dimensional vector.
func Pi(env *tempAll.Environment, k vec.Vector, omega float64) vec.Vector {
var piInner func(k vec.Vector, out *vec.Vector)
// TODO: should this comparison be math.Abs(env.F0)? Not using that to
// avoid going to finite F0 procedure when F0 < 0 (since F0 is
// positive by choice of gauge). Also - would it be better to just
// test if F0 == 0.0? Would prefer to avoid equality comparison
// on float.
if math.Abs(env.F0) < 1e-9 {
piInner = func(q vec.Vector, out *vec.Vector) {
// do vector operations on out to avoid allocation:
// out = k/2 + q
(*out)[0] = k[0]/2.0 + q[0]
(*out)[1] = k[1]/2.0 + q[1]
xp := env.Xi_h(*out)
// out = k/2 - q
(*out)[0] = k[0]/2.0 - q[0]
(*out)[1] = k[1]/2.0 - q[1]
xm := env.Xi_h(*out)
tp := math.Tanh(env.Beta * xp / 2.0)
tm := math.Tanh(env.Beta * xm / 2.0)
common := -(tp + tm) / (omega - xp - xm)
sx := math.Sin(q[0])
sy := math.Sin(q[1])
// out = result
(*out)[0] = sx * sx * common
(*out)[1] = sx * sy * common
(*out)[2] = sy * sy * common
}
} else {
piInner = func(q vec.Vector, out *vec.Vector) {
// out = k/2 + q
(*out)[0] = k[0]/2.0 + q[0]
(*out)[1] = k[1]/2.0 + q[1]
xi1 := env.Xi_h(*out)
E1 := env.BogoEnergy(*out)
// out = k/2 - q
(*out)[0] = k[0]/2.0 - q[0]
(*out)[1] = k[1]/2.0 - q[1]
xi2 := env.Xi_h(*out)
E2 := env.BogoEnergy(*out)
A1 := 0.5 * (1.0 + xi1/E1)
A2 := 0.5 * (1.0 + xi2/E2)
B1 := 0.5 * (1.0 - xi1/E1)
B2 := 0.5 * (1.0 - xi2/E2)
t1 := math.Tanh(env.Beta * E1 / 2.0)
t2 := math.Tanh(env.Beta * E2 / 2.0)
common := -(t1+t2)*(A1*A2/(omega-E1-E2)-B1*B2/(omega+E1+E2)) - (t1-t2)*(A1*B2/(omega-E1+E2)-B1*A2/(omega+E1-E2))
sx := math.Sin(q[0])
sy := math.Sin(q[1])
// out = result
(*out)[0] = sx * sx * common
(*out)[1] = sx * sy * common
(*out)[2] = sy * sy * common
}
}
return bzone.VectorAvg(env.PointsPerSide, 2, 3, piInner)
}
func innerX1(env *tempAll.Environment, k vec.Vector) float64 {
return env.Fermi(env.Xi_h(k))
}
func innerBeta(env *tempAll.Environment, k vec.Vector) float64 {
sxy := math.Sin(k[0]) - math.Sin(k[1])
return sxy * sxy * math.Tanh(env.Beta*env.Xi_h(k)/2.0) / env.Xi_h(k)
}
func innerMu_hNoninteracting(env *tempAll.Environment, k vec.Vector) float64 {
return env.Fermi(env.Xi_h(k))
}
func innerMu_h(env *tempAll.Environment, k vec.Vector) float64 {
return (1.0 - env.Xi_h(k)/env.BogoEnergy(k)) / 2.0
}
func innerD1(env *tempAll.Environment, k vec.Vector) float64 {
sxy := math.Sin(k[0]) * math.Sin(k[1])
E := env.BogoEnergy(k)
return sxy * (1.0 - env.Xi_h(k)*math.Tanh(env.Beta*E/2.0)/E)
}
func innerD1(env *tempAll.Environment, k vec.Vector) float64 {
return math.Sin(k[0]) * math.Sin(k[1]) * env.Fermi(env.Xi_h(k))
}
func innerX1(env *tempAll.Environment, k vec.Vector) float64 {
E := env.BogoEnergy(k)
return 1.0 - env.Xi_h(k)*math.Tanh(env.Beta*E/2.0)/E
}
func innerD1Noninteracting(env *tempAll.Environment, k vec.Vector) float64 {
sxy := math.Sin(k[0]) * math.Sin(k[1])
return -sxy * env.Fermi(env.Xi_h(k))
}
func innerD1(env *tempAll.Environment, k vec.Vector) float64 {
sxy := math.Sin(k[0]) * math.Sin(k[1])
return -sxy * (1.0 - env.Xi_h(k)/env.BogoEnergy(k)) / 2.0
}