bb, osc = getBoundary(rhoSol[osci][0], rhoSol[osci][1], [0, a2])
mu = bb[1][0]
def f(l):
w = np.exp(l)
bb, osc = getBoundary(rhoSol[osci][0], rhoSol[osci][1], [mu * w, a2])
assert osc == osci
return -1j * bb[2][1] / (bb[2][0] * (mu * w))
nwvs, _, nsigmas = getPlotY(np.log(wvs[0]), np.log(wvs[-1]), f, lambda s: s.real, minN=150, maxTurn=0.1)
sigmas.append((np.exp(nwvs), nsigmas))
for s in sigmas:
pl.plot(s[0], [i.real for i in s[1]], ls="-", c="k", label=r"$\mathrm{Re}(\sigma)$" if first else "")
if a2 == 0:
printText(
s[0], [i.real for i in s[1]], [2, 0.8, 0.35, 0.25][j], [-1 / 0.35, 0, 0, 0][j], "$" + str(Tr) + "T_c$"
)
else:
if (j / 2) * 2 == j or len(Trs) < 8:
B = 1e6
# printText(s[0],[i.real for i in s[1]],B,-B/(0.35 if j==0 else 0.27),'$'+str(Tr)+'T_c$')
# printText(s[0],[i.real for i in s[1]],1/(1-0.25/0.4),-1/(0.4-0.25),'$'+str(Tr)+'T_c$')
printText(
s[0], [i.real for i in s[1]], 1 / (1 - 0.23 / 0.308), -1 / (0.308 - 0.23), "$" + str(Tr) + "T_c$"
)
if plotImag:
pl.plot(s[0], [i.imag for i in s[1]], ls="--", c="k", label=r"$\mathrm{Im}(\sigma)$" if first else "")
printText(
s[0], [i.imag for i in s[1]], [1, 0.25, 1.25, -0.7][j], [-1 / 0.58, 0, 0, 0][j], "$" + str(Tr) + "T_c$"
)
first = False
rhoSol=findrho(lambda x,y: getBoundary(x,y,[0,a2]), sols, hpsis, bbs, murs[j]*T,ind=0)
print('Solving for different frequencies...')
sigmas=[]
for osci in range(len(rhoSol)):
bb,osc=getBoundary(rhoSol[osci][0],rhoSol[osci][1], [0,a2])
def f(w):
bb,osc=getBoundary(rhoSol[osci][0],rhoSol[osci][1], [w*T,a2])
assert(osc==osci)
return -1j*bb[2][1]/( bb[2][0]*(T*w) )
nwvs,_,nsigmas=getPlotY(wvs[0],wvs[-1],f,lambda s:s.real*natTK,minN=60,maxTurn=0.1,maxN=150)
sigmas.append((nwvs,nsigmas))
for s in sigmas:
fig(0)
pl.plot([w*natTK for w in s[0]],[i.real for i in s[1]],ls='-',c='k')
printText([w*natTK for w in s[0]],[i.real for i in s[1]],0.6,0,'$'+str(nature[j])+'\mathrm{V}$')
if plotImag:
fig(1)
pl.plot([w*natTK for w in s[0]],[i.imag for i in s[1]],ls='-',c='k')
printText([w*natTK for w in s[0]],[i.imag for i in s[1]],0.6,0,'$'+str(nature[j])+'\mathrm{V}$')
first=False
print('$\mu_0=%.1fT$'%(murs[0]/nature[0]))
#pl.plot([wvs[0],wvs[-1]],[1,1],ls=':',c='k')
#pl.plot([wvs[0],wvs[-1]],[0,0],ls=':',c='k')
#printText([wvs[0],wvs[-1]],[1,1],0,5.,r'$\sigma=1$')
#pl.legend(loc=3)
#pl.legend(loc='upper right')
fig(0)
pl.xlabel(r'$\omega\ [\mathrm{cm}^{-1}$]')
pl.ylabel(r'$\mathrm{Re}(\sigma)$')
Tc = T * np.sqrt(rho / rhoc)
bb, osc = getBoundary(1, 0, [0, a2])
guess = rho / (-bb[1][1])
from scipy.optimize import fsolve
hphi = fsolve(lambda hphi: rho + getBoundary(hphi, 0, [0, a2])[0][1][1], guess)
w = 1e-3 * Tc
bb, osc = getBoundary(hphi, 0, [w, a2])
assert osc == 0
sigma = -1j * bb[2][1] / (bb[2][0] * w)
sigma0 = sigma.real
tauTc = sigma.imag / (w * sigma0)
y1s[-1].append(sigma0)
y2s[-1].append(1 / tauTc)
fig(0, size=12)
pl.xscale("log")
pl.yscale("log")
pl.xlim(Trs[0], Trs[-1])
pl.ylim(5e-3, 2e4)
for j in range(len(a2s)):
pl.plot(Trs, [y[j] for y in y2s], ls="-", c="k", label=r"$\frac{1}{\tau T_c}$")
printText(Trs, [y[j] for y in y2s], 10.0, -0.03, "$10^{" + str(j - 4) + "}L^4$")
pl.xlabel(r"$\frac{T}{T_c}$")
pl.ylabel(r"$\frac{1}{\tau T_c}$")
# pl.legend(loc='upper left')
saveFig("scatvsT_2")
pl.show()
w=1e-3*Tc
bb,osc=getBoundary(hphi,0,[w,a2])
assert osc==0
sigma=-1j*bb[2][1]/( bb[2][0]*w )
sigma0=sigma.real
tauTc=sigma.imag/(w*sigma0)
y1s[-1].append(sigma0)
y2s[-1].append(1/tauTc)
#drude=1/(d-m*1j*w)
fig(0,size=11)
pl.xscale('log')
pl.yscale('log')
for j in range(len(Trs)):
pl.plot([a2 for a2 in a2s],y1s[j],ls='-',c='k',label=r'$\sigma_0$')
printText(a2s,y1s[j],100.,0,'$'+str(Trs[j])+'T_c$')
pl.xlabel(r'$\frac{\alpha_2}{L^4}$')
pl.ylabel(r'$\sigma_0$')
ai=50
#pl.legend(loc='upper left')
pl.xlim(a2s[0],a2s[-1])
saveFig('drudeVarMT_sigma0')
fig(1,size=11)
pl.xscale('log')
pl.yscale('log')
pl.xlim(a2s[0],a2s[-1])
for j in range(len(Trs)):
pl.plot(a2s,y2s[j],ls='-',c='k',label=r'$\sigma_0$')
printText(a2s,y2s[j],10.,0,'$'+str(Trs[j])+'T_c$')
pl.xlabel(r'$\frac{\alpha_2}{L^4}$')
first=True
j=0
for Tr in Trs:
print('Solving for specific temperature...')
rho=rhoc/Tr**2
Tc=T*np.sqrt(rho/rhoc)
rhoSol=findrho(lambda x,y: getBoundary(x,y,[0,1]), sols, hpsis, bbs, rho)
print('Solving for different frequencies...')
sigmas=[]
for osci in range(len(rhoSol)):
sigmas.append([])
for wvi in range(len(wvs)):
printRatio(osci*len(wvs)+wvi,len(rhoSol)*len(wvs))
bb,_=getBoundary(rhoSol[osci][0],rhoSol[osci][1], [Tc*wvs[wvi],1])
sigmas[-1].append(-1j*bb[2][1]/( bb[2][0]*(Tc*wvs[wvi]) ))
for s in sigmas:
pl.plot(wvs,[i.real for i in s],ls='-',c='k',label=r'$\mathrm{Re}(\sigma)$'if first else '')
printText(wvs,[i.real for i in s],[.45,0.3,0.2][j],0,'$'+str(Tr)+'T_c$')
pl.plot(wvs,[i.imag for i in s],ls='--',c='k',label=r'$\mathrm{Im}(\sigma)$'if first else '')
printText(wvs,[i.imag for i in s],[1.25,1.25,-0.7][j],0,'$'+str(Tr)+'T_c$')
first=False
j+=1
pl.plot([wvs[0],wvs[-1]],[1,1],ls=':',c='k')
pl.plot([wvs[0],wvs[-1]],[0,0],ls=':',c='k')
#printText([wvs[0],wvs[-1]],[1,1],0,5.,r'$\sigma=1$')
pl.legend(loc=3)
pl.xlabel(r'$\frac{\omega}{T_c}$')
saveFig('cond_Ts')
pl.show()
