def summand(e, L, nna, nnk, nk, gamma, x2, l1, m1, l2, m2, alpha, Ytype='r'):
nnA = nna
nnK = nnk
nnb = -1 * (np.add(nnA, nnK))
if (nk == 0):
rr = nnA
else:
factor = (1 / (2 * gamma) +
(1 / gamma - 1) * mydot(nnA, nnK) / square(nk))
rr = np.add(nnA, factor * nnK)
rr2 = mydot(rr, rr)
twopibyL = 2 * math.pi / L
a = norm(nnA) * twopibyL
b = norm(nnb) * twopibyL
Ylmlm = 1
if l1 == 2:
#Ylmlm = defns.y2(rr,m1,Ytype)
Ylmlm = defns.y2real(rr, m1)
if l2 == 2:
#Ylmlm = Ylmlm * defns.y2(rr,m2,Ytype)
Ylmlm = Ylmlm * defns.y2real(rr, m2)
exponential = exp(alpha * (x2 - rr2))
out = Ylmlm * exponential / (x2 - rr2)
# if (Ytype=='r' or Ytype=='real') and abs(out.imag)>1e-15:
# sys.exit('Error in summand: imaginary part in real basis')
return out.real
def K3cubicA(E, pvec, lp, mp, kvec, l, m):
p = norm(pvec)
k = norm(kvec)
Ep = defns.E2k(E, p)
Ek = defns.E2k(E, k)
wp = defns.omega(p)
wk = defns.omega(k)
ap = defns.qst(E, p)
a = defns.qst(E, k)
pterm = E * wp - 3
kterm = E * wk - 3
if lp == l == mp == m == 0:
D3p = Ep**2 - 4
D3 = Ek**2 - 4
out = D3p**3 + D3**3 + 2 * (pterm**3 + kterm**3) + 8 * E**2 * (
pterm * (p * ap / Ep)**2 + kterm * (k * a / Ek)**2)
elif lp == 0 and l == 2:
#out = 16/5 * kterm * (E*a/Ek)**2 * defns.y2real(kvec,m)
out = 16 / 5 * kterm * (E / Ek)**2 * defns.y2real(
kvec, m) # removed a=qk* factor (no q)
elif lp == 2 and l == 0:
#out = 16/5 * pterm * (E*ap/Ep)**2 * defns.y2real(pvec,m)
out = 16 / 5 * pterm * (E / Ep)**2 * defns.y2real(
pvec, mp) # removed ap=qp* factor (no q)
else:
out = 0
#out *= ap**lp * a**l # q factors are NOT included here (no q)
if out.imag > 1e-15:
print('Error: imaginary part in K3cubicA')
return out.real
def G(e, L, nnp, nnk, l1, m1, l2, m2):
p = sums.norm(nnp) * 2. * math.pi / L
k = sums.norm(nnk) * 2. * math.pi / L
# pk = sums.norm(np.add(nnk,nnp)) * 2. *math.pi/L
pk = sums.norm(np.add(nnk, nnp)) * 2. * math.pi / L
omp = npsqrt(1 + square(p))
omk = npsqrt(1 + square(k))
#ompk = np.sqrt(1+pk**2)
bkp2 = (e - omp -
omk)**2 - (2 * math.pi / L)**2 * sums.norm(np.add(nnk, nnp))**2
# print('test')
# nnps and nnks are the full vectors p* and k*
nnps = boost(np.multiply(nnp, 2 * math.pi / L),
np.multiply(nnk, 2 * math.pi / L), e)
nnks = boost(np.multiply(nnk, 2 * math.pi / L),
np.multiply(nnp, 2 * math.pi / L), e)
#ps = sums.norm(nnps)
#ks = sums.norm(nnks)
qps2 = square(e - omp) / 4 - square(p) / 4 - 1
qks2 = square(e - omk) / 4 - square(k) / 4 - 1
# TB: Choose spherical harmonic basis
Ytype = 'r' # 'r' for real, 'c' for complex
Ylmlm = 1
momfactor1 = 1
momfactor2 = 1
if (l1 == 2):
#momfactor1 = (ks)**l1/qps2
momfactor1 = qps2**(-l1 / 2) # TB: ks**l1 included in my y2(nnks)
#Ylmlm = y2(nnks,m1,Ytype)
Ylmlm = y2real(nnks, m1)
if (l2 == 2):
#momfactor2 = (ps)**l2/qks2
momfactor2 = qks2**(-l2 / 2) # TB: ps**l2 included in my y2(nnps)
#Ylmlm = Ylmlm * y2(nnps,m2,Ytype)
Ylmlm = Ylmlm * y2real(nnps, m2)
#out = sums.hh(e,p)*sums.hh(e,k)/(L**3 * 4*omp*omk*(bkp2-1)) *Ylmlm * momfactor1 * momfactor2
out = sums.hh(e, p) * sums.hh(e, k) / (L**3 * 4 * omp * omk *
(bkp2 - 1)) * Ylmlm # TB, no q
# if (Ytype=='r' or Ytype=='real') and abs(out.imag)>1e-15:
# sys.exit('Error in G: imaginary part in real basis output')
return out.real
def wddmp(E, pvec, lp, mp, kvec, l, m, Ytype='r'):
if lp == mp == 0:
k = norm(kvec)
p12sk = p12stark(E, pvec, kvec)
if l == m == 0:
return 1 / 3 * (qst(E, k) * norm(p12sk))**2
elif l == 2:
#return 2/15 * qst(E,k)**2 * conj(y2(p12sk,m,Ytype))
# return 2/15 * conj(y2(p12sk,m,Ytype)) # TB, no q
return 2 / 15 * conj(y2real(p12sk, m)) # TB, no q
else:
return 0
def wds(E, pvec, lp, mp, kvec, l, m, Ytype='r'):
if lp == mp == 0:
k = norm(kvec)
p = norm(pvec)
psk = pstark(E, pvec, kvec)
if l == m == 0:
return 1 / 2 * (E * omega(p) - sqrt(wss(E, pvec, 0, 0, kvec, 0, 0))
)**2 + 2 / 3 * (qst(E, k) * norm(psk))**2
elif l == 2:
#return 4/15 * qst(E,k)**2 * conj(y2(psk,m,Ytype))
# return 4/15 * conj(y2(psk,m,Ytype)) # TB, no q
return 4 / 15 * conj(y2real(psk, m)) # TB, no q
else:
return 0