# non-resonant leptogenesis with two decaying sterile neutrino using the density matrix equations. Equations from 1112.4528
import ulysses
import numpy as np
from odeintw import odeintw
from numba import jit
@jit
def fast_RHS(y0, eps1tt,eps1mm,eps1ee,eps1tm,eps1te,eps1me,eps2tt,eps2mm,eps2ee,eps2tm,eps2te,eps2me,C,d1,d2,w1,w2,n1eq,n2eq,W):
N1, N2, Ntt, Nmm, Nee, Ntm, Nte, Nme = y0
widtht,widthm = W
c1t,c1m,c1e,c2t,c2m,c2e = C
c1tc = np.conjugate(c1t)
c1mc = np.conjugate(c1m)
c1ec = np.conjugate(c1e)
c2tc = np.conjugate(c2t)
c2mc = np.conjugate(c2m)
c2ec = np.conjugate(c2e)
#define the different RHSs for each equation
rhs1 = -d1*(N1-n1eq)
rhs2 = -d2*(N2-n2eq)
rhs3 = (eps1tt * d1 * (N1-n1eq) + eps2tt * d2 * (N2-n2eq)
- 0.5 * w1 * (2 * c1t * c1tc * Ntt + c1m * c1tc * Ntm + c1e * c1tc * Nte
+ np.conjugate(c1m * c1tc * Ntm + c1e * c1tc * Nte))
- 0.5 * w2 * (2 * c2t * c2tc * Ntt + c2m * c2tc * Ntm + c2e * c2tc * Nte
+ np.conjugate(c2m * c2tc * Ntm + c2e * c2tc * Nte)))
rhs4 = (eps1mm * d1 * (N1-n1eq) + eps2mm * d2 * (N2-n2eq)
- 0.5 * w1 * (2 * c1m * c1mc * Nmm + c1m * c1tc * Ntm + c1e * c1mc * Nme
+ np.conjugate(c1m * c1tc * Ntm + c1e * c1mc * Nme))
- 0.5 * w2 * (2 * c2m * c2mc * Nmm + c2m * c2tc * Ntm + c2e * c2mc * Nme
+ np.conjugate(c2m * c2tc * Ntm + c2e * c2mc * Nme)))
rhs5 = (eps1ee * d1 * (N1-n1eq) + eps2ee * d2 * (N2-n2eq)
- 0.5 * w1 * (2 * c1e * c1ec * Nee + c1e * c1mc * Nme + c1e * c1tc * Nte
+ np.conjugate(c1e * c1mc * Nme + c1e * c1tc * Nte))
- 0.5 * w2 * (2 * c2e * c2ec * Nee + c2e * c2mc * Nme + c2e * c2tc * Nte
+ np.conjugate(c2e * c2mc * Nme + c2e * c2tc * Nte)))
rhs6 = (eps1tm * d1 * (N1-n1eq) + eps2tm * d2 * (N2-n2eq)
- 0.5 * w1 * (c1t * c1mc * Nmm + c1e * c1mc * Nte + c1m * c1mc * Ntm + c1mc * c1t * Ntt
+ c1t * c1tc * Ntm + c1t * c1ec * np.conjugate(Nme))
- 0.5 * w2 * (c2t * c2mc * Nmm + c2e * c2mc * Nte + c2m * c2mc * Ntm + c2mc * c2t * Ntt
+ c2t * c2tc * Ntm + c2t * c2ec * np.conjugate(Nme))
- widtht * Ntm - widthm * Ntm)
rhs7 = (eps1te * d1 * (N1-n1eq) + eps2te * d2 * (N2-n2eq)
- 0.5 * w1 * (c1t * c1ec * Nee + c1e * c1ec * Nte + c1m * c1ec * Ntm
+ c1t * c1ec * Ntt + c1t * c1mc * Nme + c1t * c1tc * Nte)
- 0.5 * w2 * (c2t * c2ec * Nee + c2e * c2ec * Nte + c2m * c2ec * Ntm
+ c2t * c2ec * Ntt + c2t * c2mc * Nme + c2t * c2tc * Nte)
- widtht * Nte)
rhs8 = (eps1me * d1 * (N1-n1eq) + eps2me * d2 * (N2-n2eq)
- 0.5 * w1 * (c1m * c1ec * Nee + c1e * c1ec * Nme + c1m * c1ec * Nmm
+ c1t * c1ec * np.conjugate(Ntm) + c1m * c1mc * Nme + c1m * c1tc * Nte)
- 0.5 * w2 * (c2m * c2ec * Nee + c2e * c2ec * Nme + c2m * c2ec * Nmm
+ c2t * c2ec * np.conjugate(Ntm) + c2m * c2mc * Nme + c2m * c2tc * Nte)
- widthm * Nme)
RHStemp = [rhs1, rhs2, rhs3, rhs4, rhs5, rhs6, rhs7, rhs8]
return RHStemp
[docs]class EtaB_2DME(ulysses.ULSBase):
"""
Density matrix equation (DME) with two decaying steriles. See arxiv:1112.4528.
"""
[docs] def RHS(self, y0, zzz, ETA, C, K, W):
eps1tt,eps1mm,eps1ee,eps1tm,eps1te,eps1me,eps2tt,eps2mm,eps2ee,eps2tm,eps2te,eps2me = ETA
k1term,k2term = K
if zzz != self._currz or zzz == self.zmin:
self._d1 = np.real(self.DS(k1term, zzz))
self._w1 = self.scat(zzz)*np.real(self.W1(k1term, zzz))
self._d2 = np.real(self.D2(k2term, zzz))
self._w2 = np.real(self.W2(k2term, zzz))
self._n1eq = self.N1Eq(zzz)
self._n2eq = self.N2Eq(zzz)
self._currz=zzz
return fast_RHS(y0, eps1tt,eps1mm,eps1ee,eps1tm,eps1te,eps1me,eps2tt,eps2mm,eps2ee,eps2tm,eps2te,eps2me, C,self._d1,self._d2,self._w1,self._w2,self._n1eq,self._n2eq,W)
@property
def EtaB(self):
#Define fixed quantities for BEs
_ETA = [
np.real(self.epsilon1ab(2,2)),
np.real(self.epsilon1ab(1,1)),
np.real(self.epsilon1ab(0,0)),
self.epsilon1ab(2,1) ,
self.epsilon1ab(2,0) ,
self.epsilon1ab(1,0),
np.real(self.epsilon2ab(2,2)),
np.real(self.epsilon2ab(1,1)),
np.real(self.epsilon2ab(0,0)),
self.epsilon2ab(2,1) ,
self.epsilon2ab(2,0) ,
self.epsilon2ab(1,0),
]
_C = [ self.c1a(2), self.c1a(1), self.c1a(0),
self.c2a(2), self.c2a(1), self.c2a(0)]
_K = [np.real(self.k1), np.real(self.k2)]
_W = [ 485e-10*self.MP/self.M1, 1.7e-10*self.MP/self.M1]
y0 = np.array([0+0j,0+0j,0+0j,0+0j,0+0j,0+0j,0+0j,0+0j], dtype=np.complex128)
ys, _ = odeintw(self.RHS, y0, self.zs, args = tuple([_ETA, _C , _K, _W]), full_output=1)
nb = np.real(self.sphalfact*(ys[-1,2]+ys[-1,3]+ys[-1,4]))
self.ys = np.real(ys[:, [2,3,4]])
return np.real(nb)