def P_A1_o(shell):
shell = list(shell)
No = len(defns.shell_nnk_list(shell))
one_mat = np.ones((No, No)) / No
Pk = A1_little_group_sum(shell)
U_block_list = []
for p in defns.shell_nnk_list(shell):
p = list(p)
U_block_list.append(GT.Dmat(GT.Rvec(p, shell)))
U = block_diag(*U_block_list)
return U @ np.kron(one_mat, Pk) @ U.T
def P_irrep_o_l(shell, l, I, lblock=False):
nnk_list = defns.shell_nnk_list(shell)
Lk = GT.little_group(shell)
d_I = GT.irrep_dim(I)
P_shell = []
for k2 in nnk_list:
R20 = GT.Rvec(k2, shell)
P_k2 = []
for k1 in nnk_list:
R01 = GT.Rvec(shell, k1)
P_block = np.zeros((6, 6))
for R in Lk:
RRR = GT.R_prod(R20, R, R01)
if l == 0:
P_block[0, 0] += GT.chi(RRR, I)
elif l == 2:
P_block[1:, 1:] += GT.chi(RRR, I) * GT.Dmat(RRR)[1:, 1:]
P_block = defns.chop(P_block)
P_k2.append(P_block)
P_shell.append(P_k2)
out = d_I / 48 * np.block(P_shell)
if lblock == True:
if l == 0:
return l0_proj(out)
elif l == 2:
return l2_proj(out)
else:
return out
def P_A1_o_naive(shell):
Nk = len(defns.shell_nnk_list(shell))
P_shell = np.zeros((6 * Nk, 6 * Nk))
for R in GT.Oh_list():
P_shell += np.kron(GT.Smat(R, shell).T, GT.Dmat(R))
P_shell = P_shell / 48
return P_shell
def Fmat00(E,L,alpha):
shells = shell_list(E,L)
F_list = []
for nnk in shells:
F_list += [sums.F2KSS(E,L,nnk,0,0,0,0,alpha)] * len(shell_nnk_list(nnk))
return np.diag(F_list)
def Gmat_div():
out = np.zeros((42,42))
nnk_list = [(0,0,0)]+defns.shell_nnk_list([0,0,1])
for i in range(42):
nnp = nnk_list[i//6]
[l1,m1] = defns.lm_idx(i)
for j in range(42):
nnk = nnk_list[j//6]
[l2,m2] = defns.lm_idx(j)
out[i,j] = G_div(nnp,l1,m1,nnk,l2,m2)
return out
def Fmat00(E, L, alpha, IPV=0):
shells = shell_list(E, L)
F_list = []
for nnk in shells:
nk = sums.norm(nnk)
k = nk * 2 * math.pi / L
hhk = sums.hh(E, k)
omk = sqrt(1. + k**2)
F_list += [(sums.F2KSS(E, L, nnk, 0, 0, 0, 0, alpha) + hhk * IPV /
(32 * math.pi * 2 * omk))] * len(shell_nnk_list(nnk))
# print(F_list)
return np.diag(F_list)
def Fmat_div():
out = np.zeros((42,42))
nnk_list = [(0,0,0)]+defns.shell_nnk_list([0,0,1])
for n in range(len(nnk_list)):
nnk = nnk_list[n]
for i1 in range(6):
i = 6*n+i1
[l1,m1] = defns.lm_idx(i1)
for i2 in range(6):
j = 6*n+i2
[l2,m2] = defns.lm_idx(i2)
out[i,j] = F_div(nnk,l1,m1,nnk,l2,m2)
return out
def Smat(R, shell):
R = list(R)
shell = list(shell)
nnk_list = defns.shell_nnk_list(shell)
nnk_list = [list(nnk) for nnk in nnk_list]
Nk = len(nnk_list)
S = np.zeros((Nk, Nk))
for i in range(Nk):
k = nnk_list[i]
kR = [np.sign(R[j]) * k[abs(R[j]) - 1] for j in range(3)]
j = nnk_list.index(kR)
S[i][j] = 1
return S