def eval_cross_section(interactionfile,
spinfile,
lattice,
arg,
tau_list,
h_list,
k_list,
l_list,
w_vect_list,
direction,
temperature,
kmin,
kmax,
steps,
eief,
efixed=14.7):
"""
Calculates the cross_section given the following parameters:
interactionfile, spinfile - files to get atom data
lattice - Lattice object from tripleaxisproject
arg - reduced list of operator combinations
tau_list - list of tau position
w_list - list of w's probed
direction - direction of scan
temp - temperature
kmin - minimum value of k to scan
kmax - maximum value of k to scan
steps - number of steps between kmin, kmax
eief - True if the energy scheme is Ei - Ef, False if it is Ef - Ei
efixed - value of the fixed energy, either Ei or Ef
"""
# Read files, get atom_list and such
atom_list, jnums, jmats, N_atoms_uc = readFiles(interactionfile, spinfile)
N_atoms = len(atom_list)
N = N_atoms
# TEMPORARY TO OVERRIDE ATOM_LIST ABOVE
# atom1 = atom(pos = [0.00,0,0], neighbors = [1], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom2 = atom(pos = [0.25,0,0], neighbors = [0,2], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom3 = atom(pos = [0.50,0,0], neighbors = [1,3], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom4 = atom(pos = [0.75,0,0], neighbors = [2], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom_list,N_atoms_uc = ([atom1, atom2, atom3, atom4],1)
N_atoms = len(atom_list)
# Get Hsave to calculate its eigenvalues
(Hsave, charpoly, eigs) = calculate_dispersion(atom_list,
N_atoms_uc,
N_atoms,
jmats,
showEigs=True)
print "Calculated: Dispersion Relation"
# Generate kappa's from (h,k,l)
kaprange = []
kapvect = []
if len(h_list) == len(k_list) == len(l_list):
for i in range(len(h_list)):
kappa = lattice.modvec(h_list[i], k_list[i], l_list[i],
'latticestar')
kaprange.append(kappa[0])
kapvect.append(np.array([h_list[i], k_list[i], l_list[i]]))
# kapvect.append(np.array([h_list[i]/kappa,k_list[i]/kappa,l_list[i]/kappa]))
else:
raise Exception('h,k,l not same lengths')
# Generate q's from kappa and tau
pqrange = []
mqrange = []
for tau in tau_list:
ptemp = []
mtemp = []
for kap in kapvect:
#tau = lattice.modvec(tau[0],tau[1],tau[2], 'latticestar')
ptemp.append(kap - tau)
mtemp.append(tau - kap)
pqrange.append(ptemp)
mqrange.append(mtemp)
# Calculate w_q's using q
qrange = []
# krange = []
wrange = []
if 1: # Change this later
for set in pqrange:
temp = []
temp1 = []
for q in set:
eigs = calc_eigs(Hsave, q[0] * direction['kx'],
q[1] * direction['ky'],
q[2] * direction['kz'])
# Take only one set of eigs. Should probably have a flag here.
temp.append(eigs[0])
# krange.append(np.array([q*direction['kx'], q*direction['ky'], q*direction['kz']]))
temp1.append(q)
wrange.append(temp)
qrange.append(temp1)
print "Calculated: Eigenvalues"
wrange = np.array(np.real(wrange))
qrange = np.array(np.real(qrange))
kaprange = np.array(np.real(kaprange))
print qrange.shape
print wrange.shape
print kaprange.shape
# Calculate w (not _q) as well as kp/k
w_calc = []
kpk = []
if eief == True:
for tau in tau_list:
temp = []
temp1 = []
for om in w_vect_list:
temp.append(om - efixed)
temp1.append(np.sqrt(om / efixed))
w_calc.append(temp)
kpk.append(temp1)
else:
for tau in tau_list:
temp = []
temp1 = []
for om in w_vect_list:
temp.append(-(om - efixed))
temp1.append(np.sqrt(efixed / om))
w_calc.append(temp)
kpk.append(temp1)
w_calc = np.array(np.real(w_calc))
# Grab Form Factors
ff_list = []
s = sp.Symbol('s')
for i in range(N_atoms):
el = elements[atom_list[i].atomicNum]
val = atom_list[i].valence
if val != None:
Mq = el.magnetic_ff[val].M_Q(kaprange)
else:
Mq = el.magnetic_ff[0].M_Q(kaprange)
ff_list.append(Mq)
print "Calculated: Form Factors"
# Other Constants
gamr0 = 2 * 0.2695 * 10**(-12) #sp.Symbol('gamma', commutative = True)
hbar = 1.0 # 1.05457148*10**(-34) #sp.Symbol('hbar', commutative = True)
g = 2. #sp.Symbol('g', commutative = True)
# Kappa vector
kap = sp.Symbol(
'kappa', real=True
) #spm.Matrix([sp.Symbol('kapx',real = True),sp.Symbol('kapy',real = True),sp.Symbol('kapz',real = True)])
t = sp.Symbol('t', real=True)
w = sp.Symbol('w', real=True)
W = sp.Symbol('W', real=True)
tau = sp.Symbol('tau', real=True)
q = sp.Symbol('q', real=True)
L = sp.Symbol('L', real=True)
boltz = 1. #1.3806503*10**(-23)
# Wilds for sub_in method
A = sp.Wild('A', exclude=[0, t])
B = sp.Wild('B', exclude=[0, t])
C = sp.Wild('C')
D = sp.Wild('D')
K = sp.Wild('K')
# First the exponentials are turned into delta functions:
for i in range(len(arg)):
for j in range(N):
print '1', arg[i][j]
arg[i][j] = sp.powsimp(
arg[i]
[j]) #sp.powsimp(arg[i][j], deep = True, combine = 'all')
arg[i][j] = (
arg[i][j] * exp(-I * w * t) * exp(I * kap * L)).expand(
) # * exp(I*inner_prod(spm.Matrix(atom_list[j].pos).T,kap))
arg[i][j] = sp.powsimp(
arg[i]
[j]) #sp.powsimp(arg[i][j], deep = True, combine = 'all')
# print '2', arg[i][j]
arg[i][j] = sub_in(
arg[i][j], exp(I * t * A + I * t * B + I * C + I * D + I * K),
sp.DiracDelta(A * t + B * t + C + D + K)) #*sp.DiracDelta(C))
# print '3', arg[i][j]
arg[i][j] = sub_in(
arg[i][j],
sp.DiracDelta(A * t + B * t + C * L + D * L + K * L),
sp.DiracDelta(A * hbar + B * hbar) *
sp.simplify(sp.DiracDelta(C + D + K + tau)))
# print '4', arg[i][j]
arg[i][j] = sub_in(arg[i][j],
sp.DiracDelta(-A - B) * sp.DiracDelta(C),
sp.DiracDelta(A + B) * sp.DiracDelta(C))
print '5', arg[i][j]
print "Applied: Delta Function Conversion"
# Grabs the unit vectors from the back of the lists.
unit_vect = []
kapxhat = sp.Symbol('kapxhat', commutative=False)
kapyhat = sp.Symbol('kapyhat', commutative=False)
kapzhat = sp.Symbol('kapzhat', commutative=False)
for i in range(len(arg)):
unit_vect.append(arg[i].pop())
# Subs the actual values for kx,ky,kz, omega_q and n_q into the operator combos
# The result is basically a nested list:
#
# csdata = [ op combos ]
# op combos = [ one combo per atom ]
# 1 per atom = [ evaluated exp ]
#
csdata = []
for i in range(len(arg)):
temp1 = []
for j in range(len(arg[i])):
temp2 = []
for k in range(len(tau_list)):
temp3 = []
print i, j, k
for g in range(len(qrange[k])):
pvalue = tau_list[k] + kapvect[g] + qrange[k][g]
mvalue = tau_list[k] + kapvect[g] - qrange[k][g]
if pvalue[0] == 0 and pvalue[1] == 0 and pvalue[2] == 0:
arg[i][j] = arg[i][j].subs(
sp.DiracDelta(kap + tau + q), sp.DiracDelta(0))
else:
arg[i][j] = arg[i][j].subs(
sp.DiracDelta(kap + tau + q), 0)
if mvalue[0] == 0 and mvalue[1] == 0 and mvalue[2] == 0:
arg[i][j] = arg[i][j].subs(
sp.DiracDelta(kap + tau - q), sp.DiracDelta(0))
else:
arg[i][j] = arg[i][j].subs(
sp.DiracDelta(kap + tau - q), 0)
wq = sp.Symbol('wq', real=True)
nq = sp.Symbol('n%i' % (k, ), commutative=False)
arg[i][j] = arg[i][j].subs(wq, wrange[k][g])
arg[i][j] = arg[i][j].subs(w, w_calc[k][g])
n = sp.Pow(
sp.exp(hbar * wrange[k][g] / boltz * temperature) - 1,
-1)
arg[i][j] = arg[i][j].subs(nq, n)
temp3.append(arg[i][j])
temp2.append(temp3)
temp1.append(temp2)
csdata.append(temp1)
## print arg[i][j]
# for g in range(len(kaprange)):
# arg[i][j] = arg[i][j].subs(kap, kaprange[g])
# for g in range(len(krange)):
## print 'calculating'
# temp3 = []
# wg = sp.Symbol('w%i'%(g,), real = True)
# ng = sp.Symbol('n%i'%(g,), commutative = False)
## kx = sp.Symbol('kx', real = True, commutative = True)
## ky = sp.Symbol('ky', real = True, commutative = True)
## kz = sp.Symbol('kz', real = True, commutative = True)
## arg[i][j] = arg[i][j].subs(kx,krange[g][0])
## arg[i][j] = arg[i][j].subs(ky,krange[g][1])
## arg[i][j] = arg[i][j].subs(kz,krange[g][2])
# arg[i][j] = arg[i][j].subs(wg,wrange[g])
# arg[i][j] = arg[i][j].subs(w,w_calc[g])
# nq = sp.Pow( sp.exp(hbar*wrange[g]/boltz*temp) - 1 ,-1)
# arg[i][j] = arg[i][j].subs(ng,nq)
## arg[i][j] = arg[i][j].subs(tau,tau_list[0])
#
# temp3.append(arg[i][j])
## print arg[i][j]
# temp2.append(temp3)
## print arg[i][j]
# csdata.append(temp2)
print csdata
# Front constants and stuff for the cross-section
front_constant = 1.0 # (gamr0)**2/(2*pi*hbar)
front_func = (1. / 2.) * g #*F(k)
vanderwaals = 1. #exp(-2*W)
csrange = []
if 1:
temp1 = []
temp2 = []
for q in range(len(qrange)):
print 'calculating'
for ii in range(len(csdata)):
for jj in range(len(csdata[ii])):
temp1.append(csdata[ii][jj])
# Put on gamr0, 2pi hbar, form factor, kp/k, vanderwaals first
dif = front_func**2 * front_constant # * kpk[q][0] * vanderwaals * ff_list[0][q]
# for vect in unit_vect:
# vect.subs(kapxhat,kapvect[q][0][0])
# vect.subs(kapyhat,kapvect[q][1][0])
# vect.subs(kapzhat,kapvect[q][2][0])
print 'diff', dif
print 'temp1', temp1
print sum(temp1)
dif = (dif * sum(temp1)) # * sum(unit_vect))#.expand()
csrange.append(dif)
print "Calculated: Cross-section"
csrange = np.real(csrange)
csrange = np.array(csrange)
xi = qrange
yi = wrange
zi = csrange
Z = np.zeros((xi.shape[0], yi.shape[0]))
Z[range(len(xi)), range(len(yi))] = zi
pylab.contourf(xi, yi, Z)
pylab.colorbar()
pylab.show()
def eval_cross_section(interactionfile, spinfile, lattice, arg,
tau_list, h_list, k_list, l_list, w_vect_list,
direction, temperature, kmin, kmax, steps, eief, efixed = 14.7):
"""
Calculates the cross_section given the following parameters:
interactionfile, spinfile - files to get atom data
lattice - Lattice object from tripleaxisproject
arg - reduced list of operator combinations
tau_list - list of tau position
w_list - list of w's probed
direction - direction of scan
temp - temperature
kmin - minimum value of k to scan
kmax - maximum value of k to scan
steps - number of steps between kmin, kmax
eief - True if the energy scheme is Ei - Ef, False if it is Ef - Ei
efixed - value of the fixed energy, either Ei or Ef
"""
# Read files, get atom_list and such
atom_list, jnums, jmats,N_atoms_uc=readFiles(interactionfile,spinfile)
N_atoms = len(atom_list)
N = N_atoms
# TEMPORARY TO OVERRIDE ATOM_LIST ABOVE
# atom1 = atom(pos = [0.00,0,0], neighbors = [1], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom2 = atom(pos = [0.25,0,0], neighbors = [0,2], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom3 = atom(pos = [0.50,0,0], neighbors = [1,3], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom4 = atom(pos = [0.75,0,0], neighbors = [2], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom_list,N_atoms_uc = ([atom1, atom2, atom3, atom4],1)
N_atoms = len(atom_list)
# Get Hsave to calculate its eigenvalues
(Hsave, charpoly, eigs) = calculate_dispersion(atom_list,N_atoms_uc,N_atoms,jmats,showEigs=True)
print "Calculated: Dispersion Relation"
# Generate kappa's from (h,k,l)
kaprange = []
kapvect = []
if len(h_list) == len(k_list) == len(l_list):
for i in range(len(h_list)):
kappa = lattice.modvec(h_list[i],k_list[i],l_list[i], 'latticestar')
kaprange.append(kappa[0])
kapvect.append(np.array([h_list[i],k_list[i],l_list[i]]))
# kapvect.append(np.array([h_list[i]/kappa,k_list[i]/kappa,l_list[i]/kappa]))
else:
raise Exception('h,k,l not same lengths')
# Generate q's from kappa and tau
pqrange = []
mqrange = []
for tau in tau_list:
ptemp = []
mtemp = []
for kap in kapvect:
#tau = lattice.modvec(tau[0],tau[1],tau[2], 'latticestar')
ptemp.append(kap - tau)
mtemp.append(tau - kap)
pqrange.append(ptemp)
mqrange.append(mtemp)
# Calculate w_q's using q
qrange = []
# krange = []
wrange = []
if 1: # Change this later
for set in pqrange:
temp = []
temp1 = []
for q in set:
eigs = calc_eigs(Hsave,q[0]*direction['kx'], q[1]*direction['ky'], q[2]*direction['kz'])
# Take only one set of eigs. Should probably have a flag here.
temp.append(eigs[0])
# krange.append(np.array([q*direction['kx'], q*direction['ky'], q*direction['kz']]))
temp1.append(q)
wrange.append(temp)
qrange.append(temp1)
print "Calculated: Eigenvalues"
wrange=np.array(np.real(wrange))
qrange=np.array(np.real(qrange))
kaprange=np.array(np.real(kaprange))
print qrange.shape
print wrange.shape
print kaprange.shape
# Calculate w (not _q) as well as kp/k
w_calc = []
kpk = []
if eief == True:
for tau in tau_list:
temp = []
temp1 = []
for om in w_vect_list:
temp.append(om - efixed)
temp1.append(np.sqrt(om/efixed))
w_calc.append(temp)
kpk.append(temp1)
else:
for tau in tau_list:
temp = []
temp1 = []
for om in w_vect_list:
temp.append(-(om - efixed))
temp1.append(np.sqrt(efixed/om))
w_calc.append(temp)
kpk.append(temp1)
w_calc = np.array(np.real(w_calc))
# Grab Form Factors
ff_list = []
s = sp.Symbol('s')
for i in range(N_atoms):
el = elements[atom_list[i].atomicNum]
val = atom_list[i].valence
if val != None:
Mq = el.magnetic_ff[val].M_Q(kaprange)
else:
Mq = el.magnetic_ff[0].M_Q(kaprange)
ff_list.append(Mq)
print "Calculated: Form Factors"
# Other Constants
gamr0 = 2*0.2695*10**(-12) #sp.Symbol('gamma', commutative = True)
hbar = 1.0 # 1.05457148*10**(-34) #sp.Symbol('hbar', commutative = True)
g = 2.#sp.Symbol('g', commutative = True)
# Kappa vector
kap = sp.Symbol('kappa', real = True)#spm.Matrix([sp.Symbol('kapx',real = True),sp.Symbol('kapy',real = True),sp.Symbol('kapz',real = True)])
t = sp.Symbol('t', real = True)
w = sp.Symbol('w', real = True)
W = sp.Symbol('W', real = True)
tau = sp.Symbol('tau', real = True)
q = sp.Symbol('q', real = True)
L = sp.Symbol('L', real = True)
boltz = 1.#1.3806503*10**(-23)
# Wilds for sub_in method
A = sp.Wild('A',exclude = [0,t])
B = sp.Wild('B',exclude = [0,t])
C = sp.Wild('C')
D = sp.Wild('D')
K = sp.Wild('K')
# First the exponentials are turned into delta functions:
for i in range(len(arg)):
for j in range(N):
print '1', arg[i][j]
arg[i][j] = sp.powsimp(arg[i][j])#sp.powsimp(arg[i][j], deep = True, combine = 'all')
arg[i][j] = (arg[i][j] * exp(-I*w*t) * exp(I*kap*L)).expand()# * exp(I*inner_prod(spm.Matrix(atom_list[j].pos).T,kap))
arg[i][j] = sp.powsimp(arg[i][j])#sp.powsimp(arg[i][j], deep = True, combine = 'all')
# print '2', arg[i][j]
arg[i][j] = sub_in(arg[i][j],exp(I*t*A + I*t*B + I*C + I*D + I*K),sp.DiracDelta(A*t + B*t + C + D + K))#*sp.DiracDelta(C))
# print '3', arg[i][j]
arg[i][j] = sub_in(arg[i][j],sp.DiracDelta(A*t + B*t + C*L + D*L + K*L),sp.DiracDelta(A*hbar + B*hbar)*sp.simplify(sp.DiracDelta(C + D + K + tau)))
# print '4', arg[i][j]
arg[i][j] = sub_in(arg[i][j],sp.DiracDelta(-A - B)*sp.DiracDelta(C),sp.DiracDelta(A + B)*sp.DiracDelta(C))
print '5', arg[i][j]
print "Applied: Delta Function Conversion"
# Grabs the unit vectors from the back of the lists.
unit_vect = []
kapxhat = sp.Symbol('kapxhat',commutative = False)
kapyhat = sp.Symbol('kapyhat',commutative = False)
kapzhat = sp.Symbol('kapzhat',commutative = False)
for i in range(len(arg)):
unit_vect.append(arg[i].pop())
# Subs the actual values for kx,ky,kz, omega_q and n_q into the operator combos
# The result is basically a nested list:
#
# csdata = [ op combos ]
# op combos = [ one combo per atom ]
# 1 per atom = [ evaluated exp ]
#
csdata = []
for i in range(len(arg)):
temp1 = []
for j in range(len(arg[i])):
temp2 = []
for k in range(len(tau_list)):
temp3 = []
print i,j,k
for g in range(len(qrange[k])):
pvalue = tau_list[k] + kapvect[g] + qrange[k][g]
mvalue = tau_list[k] + kapvect[g] - qrange[k][g]
if pvalue[0] == 0 and pvalue[1] == 0 and pvalue[2] == 0:
arg[i][j] = arg[i][j].subs(sp.DiracDelta(kap+tau+q),sp.DiracDelta(0))
else: arg[i][j] = arg[i][j].subs(sp.DiracDelta(kap+tau+q),0)
if mvalue[0] == 0 and mvalue[1] == 0 and mvalue[2] == 0:
arg[i][j] = arg[i][j].subs(sp.DiracDelta(kap+tau-q),sp.DiracDelta(0))
else: arg[i][j] = arg[i][j].subs(sp.DiracDelta(kap+tau-q),0)
wq = sp.Symbol('wq', real = True)
nq = sp.Symbol('n%i'%(k,), commutative = False)
arg[i][j] = arg[i][j].subs(wq,wrange[k][g])
arg[i][j] = arg[i][j].subs(w,w_calc[k][g])
n = sp.Pow( sp.exp(hbar*wrange[k][g]/boltz*temperature) - 1 ,-1)
arg[i][j] = arg[i][j].subs(nq,n)
temp3.append(arg[i][j])
temp2.append(temp3)
temp1.append(temp2)
csdata.append(temp1)
## print arg[i][j]
# for g in range(len(kaprange)):
# arg[i][j] = arg[i][j].subs(kap, kaprange[g])
# for g in range(len(krange)):
## print 'calculating'
# temp3 = []
# wg = sp.Symbol('w%i'%(g,), real = True)
# ng = sp.Symbol('n%i'%(g,), commutative = False)
## kx = sp.Symbol('kx', real = True, commutative = True)
## ky = sp.Symbol('ky', real = True, commutative = True)
## kz = sp.Symbol('kz', real = True, commutative = True)
## arg[i][j] = arg[i][j].subs(kx,krange[g][0])
## arg[i][j] = arg[i][j].subs(ky,krange[g][1])
## arg[i][j] = arg[i][j].subs(kz,krange[g][2])
# arg[i][j] = arg[i][j].subs(wg,wrange[g])
# arg[i][j] = arg[i][j].subs(w,w_calc[g])
# nq = sp.Pow( sp.exp(hbar*wrange[g]/boltz*temp) - 1 ,-1)
# arg[i][j] = arg[i][j].subs(ng,nq)
## arg[i][j] = arg[i][j].subs(tau,tau_list[0])
#
# temp3.append(arg[i][j])
## print arg[i][j]
# temp2.append(temp3)
## print arg[i][j]
# csdata.append(temp2)
print csdata
# Front constants and stuff for the cross-section
front_constant = 1.0 # (gamr0)**2/(2*pi*hbar)
front_func = (1./2.)*g#*F(k)
vanderwaals = 1. #exp(-2*W)
csrange = []
if 1:
temp1 = []
temp2 = []
for q in range(len(qrange)):
print 'calculating'
for ii in range(len(csdata)):
for jj in range(len(csdata[ii])):
temp1.append(csdata[ii][jj])
# Put on gamr0, 2pi hbar, form factor, kp/k, vanderwaals first
dif = front_func**2 * front_constant# * kpk[q][0] * vanderwaals * ff_list[0][q]
# for vect in unit_vect:
# vect.subs(kapxhat,kapvect[q][0][0])
# vect.subs(kapyhat,kapvect[q][1][0])
# vect.subs(kapzhat,kapvect[q][2][0])
print 'diff',dif
print 'temp1',temp1
print sum(temp1)
dif = (dif * sum(temp1))# * sum(unit_vect))#.expand()
csrange.append(dif)
print "Calculated: Cross-section"
csrange=np.real(csrange)
csrange=np.array(csrange)
xi=qrange
yi=wrange
zi=csrange
Z=np.zeros((xi.shape[0],yi.shape[0]))
Z[range(len(xi)),range(len(yi))]=zi
pylab.contourf(xi,yi,Z)
pylab.colorbar()
pylab.show()
def generate_cross_section(atom_list, arg, q, real_list, recip_list):
"""Generates the Cross-Section Formula for the one magnon case"""
N = len(atom_list)
gam = 1.913 #sp.Symbol('gamma', commutative = True)
r = sp.Symbol('r0', commutative=True)
h = 1. # 1.05457148*10**(-34) #sp.Symbol('hbar', commutative = True)
k = sp.Symbol('k', commutative=True)
kp = sp.Symbol('kp', commutative=True)
g = sp.Symbol('g', commutative=True)
F = sp.Function('F')
def FF(arg):
F = sp.Function('F')
if arg.shape == (3, 1) or arg.shape == (1, 3):
return sp.Symbol("%r" % (F(arg.tolist()), ), commutative=False)
kap = spm.Matrix([
sp.Symbol('kapx', commutative=False),
sp.Symbol('kapy', commutative=False),
sp.Symbol('kapz', commutative=False)
])
t = sp.Symbol('t', commutative=True)
w = sp.Symbol('w', commutative=True)
W = sp.Symbol('W', commutative=False)
kappa = sp.Symbol('kappa', commutative=False)
tau = sp.Symbol('tau', commutative=False)
# Wilds for sub_in method
A = sp.Wild('A', exclude=[0])
B = sp.Wild('B', exclude=[0])
C = sp.Wild('C')
D = sp.Wild('D')
front_constant = (gam * r)**2 / (2 * pi * h) * (kp / k) * N
front_func = (1. / 2.) * g #*F(k)
vanderwaals = exp(-2 * W)
temp2 = []
temp3 = []
temp4 = []
# Grabs the unit vectors from the back of the lists.
unit_vect = []
kapx = sp.Symbol('kapxhat', )
kapy = sp.Symbol('kapyhat', commutative=False)
kapz = sp.Symbol('kapzhat', commutative=False)
for i in range(len(arg)):
unit_vect.append(arg[i].pop())
# for ele in unit_vect:
# ele = ele.subs(kapx,spm.Matrix([1,0,0]))
# ele = ele.subs(kapy,spm.Matrix([0,1,0]))
# ele = ele.subs(kapz,spm.Matrix([0,0,1]))
# This is were the heart of the calculation comes in.
# First the exponentials are turned into delta functions:
for i in range(len(arg)):
for j in range(N):
arg[i][j] = sp.powsimp(arg[i][j], deep=True, combine='all')
arg[i][j] = arg[i][j] * exp(-I * w * t) * exp(
I * inner_prod(spm.Matrix(atom_list[j].pos).T, kap))
arg[i][j] = sp.powsimp(arg[i][j], deep=True, combine='all')
arg[i][j] = sub_in(arg[i][j], exp(I * t * A + I * t * B + C),
sp.DiracDelta(A * t + B * t +
C / I)) #*sp.DiracDelta(C))
arg[i][j] = sub_in(
arg[i][j], sp.DiracDelta(A * t + B * t + C),
sp.DiracDelta(A * h + B * h) * sp.DiracDelta(C + tau))
arg[i][j] = sub_in(arg[i][j], sp.DiracDelta(-A - B),
sp.DiracDelta(A + B))
print arg[i][j]
print "Applied: Delta Function Conversion"
# for ele in arg:
# for subele in ele:
# temp2.append(subele)
# temp3.append(sum(temp2))
#
# for i in range(len(temp3)):
# temp4.append(unit_vect[i] * temp3[i])
for k in range(len(arg)):
temp4.append(arg[k][q])
dif = (front_func**2 * front_constant * vanderwaals * sum(temp4)
) #.expand()#sp.simplify(sum(temp4))).expand()
print "Complete: Cross-section Calculation"
return dif
def generate_cross_section(atom_list, arg, q, real_list, recip_list):
"""Generates the Cross-Section Formula for the one magnon case"""
N = len(atom_list)
gam = 1.913 #sp.Symbol('gamma', commutative = True)
r = sp.Symbol('r0', commutative = True)
h = 1. # 1.05457148*10**(-34) #sp.Symbol('hbar', commutative = True)
k = sp.Symbol('k', commutative = True)
kp = sp.Symbol('kp', commutative = True)
g = sp.Symbol('g', commutative = True)
F = sp.Function('F')
def FF(arg):
F = sp.Function('F')
if arg.shape == (3,1) or arg.shape == (1,3):
return sp.Symbol("%r"%(F(arg.tolist()),),commutative = False)
kap = spm.Matrix([sp.Symbol('kapx',commutative = False),sp.Symbol('kapy',commutative = False),sp.Symbol('kapz',commutative = False)])
t = sp.Symbol('t', commutative = True)
w = sp.Symbol('w', commutative = True)
W = sp.Symbol('W', commutative = False)
kappa = sp.Symbol('kappa', commutative = False)
tau = sp.Symbol('tau', commutative = False)
# Wilds for sub_in method
A = sp.Wild('A',exclude = [0]); B = sp.Wild('B',exclude = [0]); C = sp.Wild('C'); D = sp.Wild('D');
front_constant = (gam*r)**2/(2*pi*h)*(kp/k)*N
front_func = (1./2.)*g#*F(k)
vanderwaals = exp(-2*W)
temp2 = []
temp3 = []
temp4 = []
# Grabs the unit vectors from the back of the lists.
unit_vect = []
kapx = sp.Symbol('kapxhat',)
kapy = sp.Symbol('kapyhat',commutative = False)
kapz = sp.Symbol('kapzhat',commutative = False)
for i in range(len(arg)):
unit_vect.append(arg[i].pop())
# for ele in unit_vect:
# ele = ele.subs(kapx,spm.Matrix([1,0,0]))
# ele = ele.subs(kapy,spm.Matrix([0,1,0]))
# ele = ele.subs(kapz,spm.Matrix([0,0,1]))
# This is were the heart of the calculation comes in.
# First the exponentials are turned into delta functions:
for i in range(len(arg)):
for j in range(N):
arg[i][j] = sp.powsimp(arg[i][j], deep = True, combine = 'all')
arg[i][j] = arg[i][j] * exp(-I*w*t) * exp(I*inner_prod(spm.Matrix(atom_list[j].pos).T,kap))
arg[i][j] = sp.powsimp(arg[i][j], deep = True, combine = 'all')
arg[i][j] = sub_in(arg[i][j],exp(I*t*A + I*t*B + C),sp.DiracDelta(A*t + B*t + C/I))#*sp.DiracDelta(C))
arg[i][j] = sub_in(arg[i][j],sp.DiracDelta(A*t + B*t + C),sp.DiracDelta(A*h + B*h)*sp.DiracDelta(C + tau))
arg[i][j] = sub_in(arg[i][j],sp.DiracDelta(-A - B),sp.DiracDelta(A + B))
print arg[i][j]
print "Applied: Delta Function Conversion"
# for ele in arg:
# for subele in ele:
# temp2.append(subele)
# temp3.append(sum(temp2))
#
# for i in range(len(temp3)):
# temp4.append(unit_vect[i] * temp3[i])
for k in range(len(arg)):
temp4.append(arg[k][q])
dif = (front_func**2 * front_constant * vanderwaals * sum(temp4))#.expand()#sp.simplify(sum(temp4))).expand()
print "Complete: Cross-section Calculation"
return dif