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denscheck.py
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denscheck.py
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import math
import numpy as np
import scipy
from scipy import special
from scipy import integrate
import matplotlib
from matplotlib import pylab
from pylab import *
def Pi_mono(kf,q):
#if abs(kf) < 1e-2: return q / 16.0;
pimin = np.pi * q / 8.0
kfabs = abs(kf)
if abs(q) <= 2.0 * kfabs:
piplus = kfabs - pimin
else:
piplus = kfabs - kfabs / 2.0 * np.sqrt( 1 - ((2.0*kfabs / q)**2))
piplus += -q / 4.0 * np.arcsin( 2.0 * kfabs / q)
return (pimin + piplus) / 2.0 / np.pi
if False:
qvals = np.linspace(0.0, 10.0, 1000)
figure()
for kf in [1.0, 2.0]:
pivals = np.vectorize(lambda q: Pi_mono(kf, q)) (qvals)
plot (qvals, pivals, label='kF = %g' % kf)
plot (qvals, 1.0 /16.0 * qvals, 'k--', label='kf = 0 limit')
legend()
show()
def polaris(r, Elims,Ustr,r0):
nr = len(r)
func = np.zeros(nr)
for a in range(0,nr):
def f(q):
Pi_1 = Pi_mono( Elims[1], q )
Pi_0 = Pi_mono( Elims[0], q )
dPi = Pi_1 - Pi_0
U = (2 * np.pi) * np.exp( - q * r0 ) / q * Ustr
J = special.jn( 0, q * r[a] )
return q * J * U * dPi
func[a], eps = integrate.quad(f,0,Inf)
func = func / (2*np.pi)
plot(r, func, label='polarisation operator')
return func
#
# New version of linear response code which uses
# the Fourier transform of the potential as an input
#
def polaris_generic(r, E0, Uq):
nr = len(r)
func = np.zeros(nr)
for a in range(0,nr):
def f(q):
Pi_0 = Pi_mono( E0, q )
J = special.jn( 0, q * r[a] )
return q * J * Uq(q) * Pi_0
func[a], eps = integrate.quad(f,0,Inf, limit=100)
func = func / (2*np.pi)
#plot(r, func, label='polarisation operator')
return func
if False:
#2 window Coulomb potential with r0
r0 = 1.0
rvals = np.arange(0.1, 50.0, 0.2)
def Uq_r0 (q):
return 2.0 * np.pi / q * np.exp(-q*r0)
E_2 = -1.0
E_1 = -0.5
rhovals2 = polaris_generic(rvals, E_1, Uq_r0) - polaris_generic(rvals, E_2, Uq_r0)
rhovals0 = polaris(rvals, (E_2, E_1), 1.0, r0)
plot (rvals, rhovals2, label="New")
plot (rvals, rhovals0, label="Old")
legend()
show()
if False:
#1 window Coulomb potential with r0
r0 = 1.0
E_F = 0.1
rvals = np.arange(0.1, 50.0, 0.2)
def Uq_r0 (q):
return 2.0 * np.pi / q * np.exp(-q*r0)
rhovals2 = polaris_generic(rvals, E_F, Uq_r0)
plot (rvals, rhovals2, label="New")
rho_undoped = 1.0 / 16.0 / np.sqrt(r0**2 + rvals**2)**3
plot (rvals, rho_undoped, label="Undoped")
rho_doped = abs(E_F) / 2.0 / np.pi * 1.0 / np.sqrt(r0**2 + rvals**2)
plot (rvals, rho_doped, label="Doped")
legend()
show()
def drho(r,Elims,Ustr,r0):
N = len(r)
check = np.zeros((len(r)))
Emax = Elims[1]
Emin = Elims[0]
drho = np.zeros((N))
nm = 15
r0 = 1.0
# U0 = -1 / np.sqrt(r**2+r0**2)
# U0 = -1.0 * np.exp(-0.2 * r)
# U = Ustr * U0
U =np.load("potvec-cn-U=%g-grid=%g-r0=%g.npy" %(Ustr,len(r),r0))
mdrho = np.load("mdrho-cn-U=%g-B=0-m=%d-grid=%d-E=%g-%g.npy"
%(Ustr, nm, N, Emin, Emax))
for m in range (0,nm):
drho[:] += mdrho[:,m]
difft = - (abs(Emax) - abs(Emin)) * U / (2.0 * np.pi)
plot(r, drho, label='delta rho - sim')
plot(r, difft, 'r--', label='delta rho - TF')
title('Change in charge density; U = %g, Energy window: %g to %g'
%(-Ustr, Emin, Emax))
# ylim(0,0.1)
legend()
show()
figure()
# loglog(r, 1e-2*r**(-3.0), 'k--', label='r^-3')
# loglog(r, 1e-2*r**(-2.0), 'm--', label='r^-2')
loglog(r, 1e-1*r**(-1.0), 'c--', label='r^-1')
if Ustr >= 0:
loglog(r, -drho, label='-delta rho - sim')### minus sign!
loglog(r, -difft, label='-delta rho - TF')### minus sign!
else:
loglog(r, drho, label='delta rho - sim')
loglog(r, difft, label='delta rho - TF')
title('U = %g/r Log-Log' %(-Ustr))
# legend()
# show()
return drho
if __name__ == '__main__':
r = np.load('rvec.npy')
r0 = 1.0
alpha = 0.2
Elims = np.load('Elims.npy')
print 'Elims =', Elims
#Ustr = [-1.0, -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1],
Ustr = [1.0, 0.1, -0.1, -1.0]#, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
diffs = np.zeros((len(r), len(Ustr)))
diffp = np.zeros((len(r), len(Ustr)))
ratios = np.zeros((len(r),len(Ustr)))
def Uq_Coulomb(q):
return 2.0 * np.pi / q * np.exp( - q * r0)
def Uq_exp(q):
return 2.0 * np.pi * alpha / (q**2 + alpha**2)**(1.5)
for a in range (0,len(Ustr)):
U = Ustr[a]
print "Checking: ", -U
figure()
#diffp[:,a] = polaris(r, Elims, U, r0)
if True:
diffp[:,a] = U*(polaris_generic(r, Elims[1], Uq_Coulomb)
- polaris_generic(r, Elims[0], Uq_Coulomb))
plot(r, diffp[:,a], label='polarisation operator')
diffs[:,a] = drho(r, Elims, U, r0)
ratios[:,a] = (diffs[:,a]/ U) - (diffp[:,0] / Ustr[0])
if U >= 0:
loglog(r, -diffp[:,a], label='-Polarisation Operator')### minus sign!
else:
loglog(r, diffp[:,a], label='Polarisation Operator')
legend()
show()
figure()
for a in range (0,len(Ustr)):
U = Ustr[a]
U1 = np.load("potvec-cn-U=%g-grid=%g-r0=%g.npy" %(U,len(r),r0))
plot(r, (diffs[:,a]/U), label='U = %g / r Sim' %(-U))
plot(r, (diffp[:,0]/Ustr[0]), label='Linear response U = %g / r' %(-U))
title("Change in Charge Density Over Inducing Potential")
legend()
show()
np.save("cou-linear-array", diffp)
# np.save('ratios-N=%d-m=1-E=%g-%g' %(len(r), Elims[0], Elims[1]), ratios)
figure()
# plot([r[0],r[-1]], [1,1], 'k--')
for b in range (0,len(Ustr)):
plot(r, ratios[:,b], label='U = %g' %Ustr[b])
title('Difference Simulation - Polarisation')
legend()
show()
fluff = diffp[:,a] / U
np.save('generic-linear-response-cn-r0=1.0', fluff)