def summand(e, L, nna, nnk, gamma, x2, l1, m1, l2, m2, alpha):
nk = norm(nnk)
nnA = np.array(nna)
nnK = np.array(nnk)
nnb = -1 * nnA - 1 * nnK
if (nk == 0):
rr = nnA
else:
rr = nnA + nnK / (2 * gamma) + nnK * (1 / gamma - 1) * np.dot(
nnA, nnK) / nk**2
rr2 = np.dot(rr, rr)
twopibyL = 2 * math.pi / L
a = norm(nnA) * twopibyL
b = norm(nnb) * twopibyL
# TB: Choose spherical harmonic basis
Ytype = 'r' # 'r' for real, 'c' for complex
Ylmlm = 1
if l1 == 2:
Ylmlm = defns.y2(rr, m1, Ytype)
if l2 == 2:
Ylmlm = Ylmlm * defns.y2(rr, m2, Ytype)
exponential = np.exp(alpha * (x2 - rr2))
out = Ylmlm * exponential / (x2 - rr2)
if (Ytype == 'r' or Ytype == 'real') and abs(out.imag) > 1e-15:
print('Error in summand: imaginary part in real basis')
else:
out = out.real
return out
def omega2sum(E, pvec, lp, mp, kvec, l, m, Ytype='r'):
k = LA.norm(kvec)
p = LA.norm(pvec)
if (lp == 0 and mp == 0):
if (l == 0 and m == 0):
S1 = omega(k)**2 + (
(E - omega(k))**2) / 2 + 2 / 3 * (k * qst(E, k) / E2k(E, k))**2
elif l == 2:
#S1 = 4/15*(qst(E,k) / E2k(E,k))**2 * conj(y2(kvec,m,Ytype))
S1 = 4 / 15 * (1 / E2k(E, k))**2 * conj(y2(kvec, m,
Ytype)) # TB, no q
else:
S1 = 0
else:
S1 = 0
if (l == 0 and m == 0):
if (lp == 0 and mp == 0):
S2 = omega(p)**2 + (
(E - omega(p))**2) / 2 + 2 / 3 * (p * qst(E, p) / E2k(E, p))**2
elif lp == 2:
#S2 = 4/15*(qst(E,p) / E2k(E,p))**2 * y2(pvec,mp,Ytype)
S2 = 4 / 15 * (1 / E2k(E, p))**2 * y2(pvec, mp, Ytype) # TB, no q
else:
S2 = 0
else:
S2 = 0
if np.imag(S1 + S2) > 10**-8:
print('Error: imaginary part in omega2sum')
return np.real(S1 + S2)
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
omp = np.sqrt(1 + p**2)
omk = np.sqrt(1 + k**2)
#ompk = np.sqrt(1+pk**2)
bkp2 = (e - omp -
omk)**2 - (2 * math.pi / L)**2 * sums.norm(np.add(nnk, nnp))**2
# 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 = (e - omp)**2 / 4 - p**2 / 4 - 1
qks2 = (e - omk)**2 / 4 - k**2 / 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)
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)
# 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:
print('Error in G: imaginary part in real basis output')
else:
out = out.real
return out
def wds(E,pvec,lp,mp,kvec,l,m,Ytype='r'):
if lp==mp==0:
k=LA.norm(kvec); p=LA.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)*LA.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
else:
return 0
def wddmp(E, pvec, lp, mp, kvec, l, m, Ytype):
if lp == mp == 0:
k = LA.norm(kvec)
p12sk = p12stark(E, pvec, kvec)
if l == m == 0:
return 1 / 3 * (qst(E, k) * LA.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
else:
return 0