// Evaluate the anomalous retarded pair Green's function,
// Pi^A(k, omega)_{xx, xy, yy}. k must be a two-dimensional vector.
func PiAnom(env *tempAll.Environment, k vec.Vector, omega float64) vec.Vector {
piInner := func(q vec.Vector, out *vec.Vector) {
// Do vector operations on out to avoid allocation:
// first case, out = k/2 + q
(*out)[0] = k[0]/2.0 + q[0]
(*out)[1] = k[1]/2.0 + q[1]
Delta1 := env.Delta_h(*out)
E1 := env.BogoEnergy(*out)
// second case, out = k/2 - q
(*out)[0] = k[0]/2.0 - q[0]
(*out)[1] = k[1]/2.0 - q[1]
Delta2 := env.Delta_h(*out)
E2 := env.BogoEnergy(*out)
// Get part of result that's the same for all (xx, xy, yy):
t1 := math.Tanh(env.Beta * E1 / 2.0)
t2 := math.Tanh(env.Beta * E2 / 2.0)
common := -Delta1 * Delta2 / (4.0 * E1 * E2) * ((t1+t2)*(1.0/(omega+E1+E2)-1.0/(omega-E1-E2)) + (t1-t2)*(1.0/(omega-E1+E2)-1.0/(omega+E1-E2)))
// Set out = result:
sx := math.Sin(q[0])
sy := math.Sin(q[1])
(*out)[0] = sx * sx * common
(*out)[1] = sx * sy * common
(*out)[2] = sy * sy * common
}
return bzone.VectorAvg(env.PointsPerSide, 2, 3, piInner)
}
// 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)
}
