def plot(bbs,ind,As=None,name='',verbose=False):
lss=['-', '--', '-.', ':']*4
bbs=np.array(bbs)
if As!=None: A=np.array(As)
p1=bbs[:,:,0,0].real
p2=bbs[:,:,0,1].real
mu=bbs[:,:,1,0].real
rho=-bbs[:,:,1,1].real
rhoc=min([min(r) for r in rho])#rho, in units used at Tc
if verbose: print 'rhoc: '+str(rhoc)
zh=1.#choice of length units makes zh numerically constant
T=3./(zh*4.*np.pi)#temp of solution in units used, this is constant by choice of units
for osci in range(len(rho)):
Tc=T*np.sqrt(rho[osci]/rhoc)#critical temp, in units used for all solutions
fig(1)
pl.plot(T/Tc,np.power(np.abs(p2[osci])*np.sqrt(2.),1./(ind[0][0][1]))/Tc,c='k',ls=lss[osci])
fig(4)
pl.plot(T/Tc,mu[osci]/Tc,c='k',ls=lss[osci])
if As!=None:
fig(7)
pl.plot(T/Tc,A[osci]/Tc**3,c='k',ls=lss[osci])
if verbose:
print 'mu/rho'+str(mu[osci][-1]/rho[osci][-1])
print 'p2/rho'+str(p2[osci][-1]/rho[osci][-1])
fig(1)
pl.plot([0,2], [0,0], c='k', lw=1)
pl.xlabel('$\\frac{T}{T_c}$')
pl.ylabel('$\\frac{\\sqrt{O_2}}{T_c}$')
pl.xlim([0,1.2])
pl.ylim([-1,10])
if name: saveFig(name+'O2Tzeros')
fig(4)
rho=np.linspace(rhoc*0.2,rhoc*10,1000)
mu=rho*zh
Tc=T*np.sqrt(rho/rhoc)#critical temp, in units used for all solutions
pl.plot(T/Tc,mu/Tc,c='k',ls='-',lw=1)
pl.xlabel('$\\frac{T}{T_c}$')
pl.ylabel('$\\frac{\\mu}{T_c}$')
pl.xlim([0,1.2])
pl.ylim([0,40])
if name: saveFig(name+'muTzeros')
if As!=None:
fig(7)
pl.xlabel('$\\frac{T}{T_c}$')
pl.ylabel('$\\frac{A}{V_{2}T_c^3}$')
Atriv=4*np.pi*T/3*mu**2/2
pl.plot(T/Tc, Atriv/Tc**3,c='k',ls='-',lw=1)
pl.xlim([0,2])
pl.ylim([0,1.5e3])
if name: saveFig(name+'A')
for i in range(len(ws)):
bb,osc=getBoundary(hphi,0,[Tc*ws[i],a2])
assert osc==0
sigmas.append(-1j*bb[2][1]/( bb[2][0]*(Tc*ws[i]) ))
d=1/sigmas[0].real
m=sigmas[0].imag/(Tc*ws[0])*d**2
sigma0=1/d
tau=m*sigma0
sigma0s.append(sigma0)
taus.append(tau)
ms.append(m*Tc)
fig(0)
pl.plot(a2s,sigma0s,c='k',label=r'$\sigma_0$',marker='.')
pl.plot(a2s,taus,c='k',ls='--',marker='.',label=r'$\tau$')
pl.plot(a2s,ms,c='k',ls='--',marker='.',label=r'$\tau$')
'''n=20
k=np.log(sigma0s[-1]/sigma0s[-n])/np.log(a2s[-1]/a2s[-n])
print k
m=np.log(sigma0s[-1]/a2s[-1]**k)
pl.plot([a2s[0],a2s[-1]],[np.exp(m)*a2s[0]**k,np.exp(m)*a2s[-1]**k],ls=':',c='k')
k=np.log(taus[-1]/taus[-n])/np.log(a2s[-1]/a2s[-n])
print k
m=np.log(taus[-1]/a2s[-1]**k)
pl.plot([a2s[0],a2s[-1]],[np.exp(m)*a2s[0]**k,np.exp(m)*a2s[-1]**k],ls=':',c='k')'''
pl.xlabel(r'$\alpha_2$')
pl.xscale('log')
pl.yscale('log')
pl.legend()
saveFig('drudePars')
pl.show()
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'$\mathrm{Re}(\sigma)$')
saveFig('graphene2_cond_re_a2_'+str(a2))
fig(1)
pl.xlabel(r'$\omega\ [\mathrm{cm}^{-1}$]')
pl.ylabel(r'$\mathrm{Im}(\sigma)$')
saveFig('graphene2_cond_im_a2_'+str(a2))
pl.show()
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'$\frac{\alpha_2}{L^4}$')
pl.ylabel(r'$\frac{1}{\tau T_c}$')
ai=50
#pl.legend(loc='upper left')
saveFig('drudeVarMT_tau')
pl.show()
#pl.plot(wvs,nsigma.imag)
mw=0.15
mi=int(np.interp(mw,wvs,range(len(wvs))))
Y=abs(nsigma[mi])
Yd=(abs(nsigma[mi+1])-abs(nsigma[mi-1]))/(wvs[mi+1]-wvs[mi-1])
gamma=-2./3
C=Y-Yd*wvs[mi]/gamma
B=(Y-C)/wvs[mi]**gamma
fig(0)
pl.plot(wvs,abs(nsigma)-C,c='k')
pl.plot(wvs,wvs**gamma*B,ls='--',c='red')
minAbs=min(wvs[-1]**gamma*B,minAbs)
maxAbs=max(wvs[0]**gamma*B,maxAbs)
fig(1)
pl.plot(wvs,np.arctan2(nsigma.imag,nsigma.real)/np.pi*180.)
#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)
fig(0)
pl.ylim(minAbs,maxAbs)
pl.xlabel(r'$\frac{\omega}{\mu}$')
pl.ylabel(r'$|\sigma_n|-C$')
saveFig('PL_Ts_a2_'+str(a2)+'_abs')
fig(1)
pl.xlabel(r'$\frac{\omega}{\mu}$')
pl.ylabel(r'$\mathrm{arg}(\sigma_n)$')
saveFig('PL_Ts_a2_'+str(a2)+'_arg')
pl.show()
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()
from results import loadG, loadGBenchmark, getSfun, getGfun, GlargeNfApp
import pylab as pl
import numpy as np
import matplotlib.pyplot as plt
from fig import fig, saveFig, fill_between, grid_selfmade
N=35000
wm=.021234;
colors=['red', 'green', 'blue', 'violet','yellow']
f=fig(0,size=10)
Nf=1.
kx=1
xs=np.linspace(kx-wm, kx+wm, N)
pl.plot(xs, -2*np.imag(GlargeNfApp(Nf,-1j*xs+0.000001,kx)),label='',color='black')
pl.plot(np.linspace(kx-.0005,kx+.0005,1000),500*[-120000,120000],color='black')
#pl.plot(xs, -np.imag(GlargeNfApp(Nf,-1j*xs+0.00001,kx)),label='',color='blue')
#pl.yscale('log')
pl.xlim([xs[0],xs[-1]])
#pl.legend(loc=4)
pl.ylim([-100000,100000])
grid_selfmade(f.get_axes()[0])
pl.xlabel(r'$\omega/\lambda^2$')
pl.ylabel(r'$A(\omega, k_x=\lambda^2)/\lambda^2$')
saveFig('inconsistency')
plt.show()
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
# 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")
pl.xlabel(r"$\frac{\omega}{\mu}$")
saveFig("cond_Ts_a2_" + str(a2) + "_v2")
pl.show()
printRatio(i,len(ws))
bb,osc=getBoundary(hphi,0,[Tc*ws[i],a2])
assert osc==0
sigmas.append(-1j*bb[2][1]/( bb[2][0]*(Tc*ws[i]) ))
li=0
sigma0=sigmas[li].real
tauTc=sigmas[li].imag/(ws[li]*sigma0) #tau*Tc
drude=sigma0/(1-1j*ws*tauTc)
fig(0,size=11)
pl.plot(ws,[s.real for s in sigmas],c='k',label=r'$\mathrm{AdS/CFT}$')
pl.plot(ws,[s.real for s in drude],c=[1.0,0.,0.],ls='--',label=r'$\mathrm{Drude}$')
pl.plot(ws,[s.imag for s in sigmas],c='k')
pl.plot(ws,[s.imag for s in drude],ls='--',c=[1.,0.,0.])
#pl.plot(ws,[(sigmas[si]-drude[si]).real for si in range(len(drude))],c=[1.0,0.,0.],ls='--',label=r'$\mathrm{Drude}$')
pl.xlabel(r'$\frac{\omega}{T_c}$')
pl.ylabel(r'$\sigma$')
pl.xscale('log')
ai=35
pl.annotate(r'$\mathrm{Re}(\sigma)$',xy=(ws[ai],sigmas[ai].real), xycoords='data',
xytext=(-45, -25), textcoords='offset points', fontsize=10,
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))
pl.annotate(r'$\mathrm{Im}(\sigma)$',xy=(ws[ai],sigmas[ai].imag), xycoords='data',
xytext=(-45, 25), textcoords='offset points', fontsize=10,
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=-.2"))
pl.legend()
saveFig('drude_T_'+str(Tr)+'Tc_a2_'+str(a2))
pl.show()
pl.plot(cConst/const[osci],As[osci]/Tc**3,ls='-' if sign==1 else '--',c='k')
#pl.plot(Trs,rho*zh/Tc,lw=1)
Trs=np.linspace(0.01,1.2,100)
if a2==0 and False:
pl.plot(Trs,(4*np.pi/3*T*Trs)*(min([min(r) for r in rhos])*(zh/Trs))**2/2 / T**3,lw=1,c='k')
else:
from scipy.integrate import cumtrapz
normAs=[]
for Tr in Trs:
rho=min([min(r) for r in rhos])/Tr**2
Tc=T/Tr
print rho
guess=0.1
from scipy.optimize import fsolve
hphi=fsolve(lambda hphi:rho+getBoundary(hphi,0,[0,a2])[0][1][1], guess)
_,_,(zs,y)=getBoundary(hphi, 0, [0,a2], plot=False, returnSol=True)
Al=[0]+list(cumtrapz([Lfun(*([zs[j]]+[0,a2]+y[j][:-4]+[0,0]))
for j in range(len(zs))][::-1], x=zs[::-1]))
normAs.append(Al[-1])
pl.plot(Trs,normAs/(T/Trs)**3,lw=1,c='k')
pl.ylim(0,2500)
#pl.legend(loc='upper right')
pl.xlabel(r'$\frac{T}{T_c}$')
pl.ylabel(r'$\frac{A_\mathrm{fields}}{V_2T_c^3}$')
saveFig('A_constRho_a2_'+str(a2))
pl.show()
# pl.plot(Trs,y1s,c='k',ls='-')
# pl.plot(Trs,[y1s[i]+y2s[i] for i in range(len(Trs))],c='k',ls='-')
ymin = min(y1s) * 1.2
fill_between(
Trs,
[ymin for i in Trs],
y1s,
hatch="/",
facecolor="white",
label=r"$\int_0^\infty\mathrm{Re}(\sigma_n(\omega)-1)\mathrm{d}\omega$",
) # , facecolor='blue', alpha=0.5)
fill_between(
Trs, y1s, [y1s[i] + y2s[i] for i in range(len(Trs))], hatch=r"\\", facecolor="white", label=r"$\Sigma_\delta$"
) # , facecolor='red', alpha=0.5)
pl.plot(
Trs,
[y1s[i] + y2s[i] for i in range(len(Trs))],
c="r",
ls="-",
label=r"$\Sigma_\delta+\int_0^\infty\mathrm{Re}(\sigma_n(\omega)-1)\mathrm{d}\omega$",
lw=1,
)
pl.ylim(ymin, -ymin * 0.8)
pl.xlim(Trs[0], Trs[-1])
pl.xlabel(r"$\frac{T}{T_c}$")
pl.ylabel(r"$[T_c]$")
handles, labels = pl.gca().get_legend_handles_labels()
pl.legend(handles[::-1], labels[::-1])
saveFig("sum_rule_a2" + str(a2))
pl.show()
#for j in range(len(Nfs)):
# pl.plot(xs, np.abs([GlargeNf(Nfs[j], 0, w) for w in xs]),label=(r'$N_f\rightarrow\infty$'),color=colors[j],ls='-')
#, N_fk_f='+str(Nfs[j])+'\lambda^2
#if r==1:
# pl.plot(xs, cf(SlargeNf(Nfs[j],xs)),color=colors[j],linestyle='--')
#pl.plot([],[],label=r'$k_x/\lambda^2='+wss+'$',color='white')
pl.xlim([wmin,wmax])
pl.ylim([7e-2,2e2])
grid_selfmade(f.get_axes()[0])
pl.legend(loc=1)
pl.xlabel(r'$k_x/\lambda^2$')
pl.ylabel(r'$|G(\omega=0, k_x)|/\lambda^2$')
saveFig('absG_vs_ks_L='+str(L))
#pl.show()
#sys.exit(0)
f=fig(1,size=14)
pl.plot(xs, np.abs([Gquenchedv1(w,0) for w in xs]),label=(r'$N_fk_f=0$'),color='black')
pl.plot(xs, np.abs([1/w for w in xs]),label=(r'$\lambda=0$'),color='black',ls='--')
for j in range(len(Nfs)):
pl.loglog(ws, abs(Gs[j](ws,0)),'+',label='$N_fk_f='+str(Nfs[j])+r'\lambda^2$',color=colors[j])
for j in range(len(Nfs)):
pl.plot(xs, np.abs([GlargeNf(Nfs[j], w, 0) for w in xs]),label=(r'$N_f\rightarrow\infty$'),color=colors[j],ls='-')
#, N_fk_f='+str(Nfs[j])+'\lambda^2
#if r==1:
# pl.plot(xs, cf(SlargeNf(Nfs[j],xs)),color=colors[j],linestyle='--')
#pl.plot([],[],label=r'$k_x/\lambda^2='+wss+'$',color='white')
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()
Cs.append(sigma.real/a2)
#drude=1/(d-m*1j*w)
fig(0,size=11)
k,m=np.polyfit(np.log(Trs),np.log(Cs),1)
print k
print np.exp(m)
plMin,plMax=.8*Trs[0],Trs[-1]/0.8
pl.plot([plMin,plMax],[plMin**k*np.exp(m), plMax**k*np.exp(m)],c='r',label=r'$\mathrm{Power\ fit}$')
pl.plot(Trs,Cs,ls='',marker='x',c='k',label=r'$\sigma_0$')
pl.xscale('log')
pl.yscale('log')
#pl.plot(a2s,y2s,ls='--',c='k',label=r'$\tau T_c$')
#hn=len(a2s)/4
#k=np.log(y1s[-1]/y1s[-2])/np.log(a2s[-1]/a2s[-2])
#m=y1s[-1]/a2s[-1]**k
#print(k)
#print(m)
#pl.plot([a2s[hn], a2s[-1]], [a2s[hn]**k*m, a2s[-1]**k*m],ls='-',c='r')#,label=r'$\mathrm{Power\ fit}$')
mTr=np.sqrt(Trs[0]*Trs[-1])
pl.annotate(('$$%.3f'%np.exp(m))+r'\left(\frac{T}{T_c}\right)^{'+('%.3f'%k)+'}$$',xy=(mTr,mTr**k*np.exp(m)), xycoords='data',
xytext=(-80, -40), textcoords='offset points', fontsize=10,
arrowprops=dict(arrowstyle="->"))
handles, labels = pl.gca().get_legend_handles_labels()
pl.legend(handles[::-1], labels[::-1])
pl.xlim(plMin,plMax)
pl.xlabel(r'$\frac{T}{T_c}$')
pl.ylabel(r'$$\lim_{\alpha_2}\rightarrow\infty}\frac{\sigma_0L^4}{\alpha_2}$$')
saveFig('drudeTdep_1e4')
pl.show()
guess=rho/(-bb[1][1])
from scipy.optimize import fsolve
hphi=fsolve(lambda hphi:rho+getBoundary(hphi,0,[0,a2])[0][1][1], guess)
rhoSol=[[hphi,0]]
assert(len(rhoSol)==1)
sigmas=[]
for osci in range(len(rhoSol)):
bb,osc=getBoundary(rhoSol[osci][0],rhoSol[osci][1], [0,a2])
mu=bb[1][0]
sigmas.append([])
for wvi in range(len(wvs)):
bb,osc=getBoundary(rhoSol[osci][0],rhoSol[osci][1], [mu*wvs[wvi],a2])
assert(osc==osci)
sigmas[-1].append(-1j*bb[2][1]/( bb[2][0]*(mu*wvs[wvi]) ))
for s in sigmas:
pl.plot(wvs,[i.imag for i in s],ls='-',c='k',label=r'$\mathrm{Im}(\sigma)$'if first else '')
first=False
#print( abs(sigmas[0][0].imag*wvs[0]/(sigmas[0][1].imag*wvs[1]) -1 ) )
assert( abs(sigmas[0][0].imag*wvs[0]/(sigmas[0][1].imag*wvs[1]) -1 )<0.001 )
ys.append(sigmas[0][0].imag*mu*wvs[0]*np.pi/2/Tc)
#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'$\sigma=1$')
fig(0)
pl.plot(Trs,ys,c='k',ls='-')
pl.ylim(0,max(ys)*1.1)
pl.xlabel(r'$\frac{T}{T_c}$')
pl.ylabel(r'$\frac{\sigma_s}{T_c}$')
saveFig('cond_delta')
pl.show()
if r==1:
pl.plot(xs, cf(SlargeNf(Nfs[j],xs)),color=colors[j],linestyle='--')
pl.plot(xs, cf([Squenchedv1(w,kx) for w in xs]),label=(r'$N_fk_f=0$' if i==0 else ''),color='black')
pl.plot([],[],label=r'$k_x/\lambda^2='+wss+'$',color='white')
pl.xlim([-wm,wm])
if r==1:
pl.ylim([-.11, .11])
else:
pl.ylim([-0,.09])
grid_selfmade(f.get_axes()[0])
pl.legend(loc=4)
pl.xlabel(r'$\omega/\lambda^2$')
pl.ylabel(r'$\mathrm{'+['Re','Im'][r]+'}(\Sigma(\omega, k_x))/\lambda^2$')
saveFig(['re','im'][r]+'_Sigma_vs_omega_L='+str(L))
for r in [0,1]:
f=fig(2+r,size=14)
for i in range(len(ws)):
w=ws[i]
cf=[np.real,np.imag][r]
for j in range(len(Nfs)):
pl.plot(xs, [cf(Ss[j](w,x)) for x in xs],label='$N_fk_f='+str(Nfs[j])+r'\lambda^2$' if i==0 else '',color=colors[j])
#iif r==1:
# pl.plot([-wm,wm], 2*[cf(SlargeNf(Nfs[j],w))],color=colors[j],linestyle='--')
pl.plot(xs, cf([Squenchedv1(w,kx) for kx in xs]),label=(r'$N_fk_f=0$' if i==0 else ''),color='black')
pl.plot([],[],label=r'$\omega/\lambda^2='+wss+'$',color='white')
pl.xlim([-wm,wm])
if r==0:
pl.ylim([-.11, .11])
for osci in range(len(mu)):
sign=-1 if O[osci][0]<0 else 1
Tc=T/cConst*const[osci]
fig(1)
pl.plot(cConst/const[osci],np.sqrt(sign*O[osci]*np.sqrt(2))/Tc,ls='-' if sign==1 else '--',c='k')
fig(2)
pl.plot(cConst/const[osci],mu[osci]/Tc,ls='-' if sign==1 else '--',c='k')
print O[osci]
fig(1)
pl.plot([0,1.2],[0,0],lw=1)
pl.ylim([-1,9])
#pl.legend(loc='upper right')
pl.xlabel(r'$\frac{T}{T_c}$')
pl.ylabel(r'$\frac{\sqrt{\sqrt{2}|\langle\mathcal{O}\rangle|}}{T_c}$')
saveFig('O_constRho_a2_'+str(a2))
fig(2)
Trs=np.linspace(0,1.2)[1:]
#pl.plot(Trs,rho*zh/Tc,lw=1)
pl.plot(Trs,min([min(r) for r in rho])*(zh/Trs)/T,lw=1)
#pl.plot(Trs,Trs*7.71285,ls=':')
pl.ylim([0,50])
#pl.legend(loc='upper right')
pl.xlabel(r'$\frac{T}{T_c}$')
pl.ylabel(r'$\frac{\mu}{T_c}$')
saveFig('mu_constRho_a2_'+str(a2))
pl.show()
rho=-bb[1][1]
mu=bb[1][0]
y2s.append(m/d*Tc)
#drude=1/(d-m*1j*w)
fig(0)
pl.xscale('log')
pl.yscale('log')
pl.plot([a2 for a2 in a2s],y1s,ls='-',c='k',label=r'$\sigma_0$')
pl.plot(a2s,y2s,ls='--',c='k',label=r'$\tau T_c$')
hn=len(a2s)/3.5
k=np.log(y1s[-1]/y1s[-2])/np.log(a2s[-1]/a2s[-2])
m=y1s[-1]/a2s[-1]**k
print(k)
print(m)
pl.plot([a2s[hn], a2s[-1]], [a2s[hn]**k*m, a2s[-1]**k*m],ls='--',c='r')#,label=r'$\mathrm{Power\ fit}$')
pl.annotate(r'$C\left(\frac{\alpha_2}{L^4}\right)^{'+('%.3f'%k)+'}$',xy=(a2s[hn],a2s[hn]**k*m), xycoords='data',
xytext=(-70, -14), textcoords='offset points', fontsize=10,
arrowprops=dict(arrowstyle="->"))
'''k=np.log(y2s[-1]/y2s[-2])/np.log(a2s[-1]/a2s[-2])
m=y2s[-1]/a2s[-1]**k
print(k)
print(m)
pl.plot([a2s[hn], a2s[-1]], [a2s[hn]**k*m, a2s[-1]**k*m],ls='-',c='b')#,label=r'$\mathrm{Power\ fit}$')'''
pl.xlabel(r'$\frac{\alpha_2}{L^4}$')
ai=50
pl.legend(loc='upper left')
pl.xlim(a2s[0],a2s[-1])
saveFig('drudeVara2_T='+str(Tr)+'Tc')
pl.show()
ws=np.logspace(-3,3,200)
sigmas=[]
for i in range(len(ws)):
printRatio(i,len(ws))
bb,osc=getBoundary(hphi,0,[Tc*ws[i],a2])
assert osc==0
sigmas.append(-1j*bb[2][1]/( bb[2][0]*(Tc*ws[i]) ))
d=1/sigmas[0].real
m=sigmas[0].imag/(Tc*ws[0])*d**2
drude=1/(d-m*1j*(Tc*ws))
fig(0)
pl.plot(ws,[s.real for s in sigmas],c='k',label=r'$\mathrm{AdS-CFT}$')
pl.plot(ws,[s.real for s in drude],c=[1.0,0.,0.],ls='--',label=r'$\mathrm{Drude}$')
pl.plot(ws,[s.imag for s in sigmas],c='k')
pl.plot(ws,[s.imag for s in drude],ls='--',c=[1.,0.,0.])
pl.xlabel(r'$\frac{\omega}{T_c}$')
pl.ylabel(r'$\sigma$')
pl.xscale('log')
ai=50
pl.annotate(r'$\mathrm{Re}(\sigma)$',xy=(ws[ai],sigmas[ai].real), xycoords='data',
xytext=(-45, -25), textcoords='offset points', fontsize=10,
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))
pl.annotate(r'$\mathrm{Im}(\sigma)$',xy=(ws[ai],sigmas[ai].imag), xycoords='data',
xytext=(-45, 25), textcoords='offset points', fontsize=10,
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=-.2"))
pl.legend()
saveFig('drude_2Tc_a21')
pl.show()