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Plot_fq.py
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import numpy as np
import matplotlib.pyplot as plt
from Libs.NiceColours import *
ShowOccs = True
ShowMultiOccs = True
ShowEnhance = False
ConstrainGx = False
Range = 1.4
n0 = 3.
def zeta_to_f(zeta):
if not(ConstrainGx):
f = 2 - 4/3*zeta**2 + 0.16979*zeta**3 + 0.16355*zeta**4
Gx = -f/(3*f-2)
else:
Gx = -(1+zeta**2)/2
f = 2*Gx/(3*Gx+1)
return f, Gx
def Get_kf(n=3, f=2):
return (6.*np.pi**2*n/f)**(1/3)
def IWP91(zeta):
y1 = np.maximum((1+zeta)**(1/3),1e-8)
y2 = np.maximum((1-zeta)**(1/3),1e-8)
return 0.5*(1. + (y1*y2*(y1+y2) + y1**3*np.log(y1) + y2**3*np.log(y2)
- 2.*np.log(y1+y2) ) / (2.*(1-np.log(2.))) )
def Occ(n=3, f=None, zeta=None, kFonly=False):
kf = Get_kf(n)
if not(f is None):
kff = Get_kf(n, f)
if kFonly: return kff
xx = np.array([0, kff, kff, kf*Range])
yy = np.array([f, f, 0, 0])
elif not(zeta is None):
nu, nd = n * (1+np.abs(zeta))/2, n * (1-np.abs(zeta))/2
if nd>0.:
kfu = Get_kf(nu, f=1.)
kfd = Get_kf(nd, f=1.)
if kFonly: return kfu,kfd
xx = np.array([0, kfd, kfd, kfu, kfu, kf*1.7])
yy = np.array([2, 2, 1, 1, 0, 0])
else:
if kFonly: return Get_kf(n, f=1.),0.
return Occ(n, f=1.)
else:
if kFonly: return kf
xx = np.array([0, kf, kf, kf*1.7])
yy = np.array([2, 2, 0, 0])
nTest = 0.
for k in range(1,len(xx)):
VV = (xx[k]**3 - xx[k-1]**3)/(6.*np.pi**2)
nTest += VV*yy[k]
print(nTest)
return xx, yy
if ShowOccs:
fig, ax = plt.subplots(1, 1, figsize=(6,2))
zeta = 0.5
f, Gx = zeta_to_f(zeta)
print("zeta = %.3f, Gx = %.3f, f = %.3f"%(zeta, Gx, f))
kfu, kfd = Occ(zeta=zeta, kFonly=True)
xx,yy = Occ(zeta=zeta)
ax.plot(xx, yy, color=NiceColour("Navy"), lw=3)
kf = Occ(kFonly=True)
xx,yy = Occ()
ax.plot(xx, yy, color=NiceColour("Teal"), dashes=(3,1,1,1), lw=3)
kff = Occ(f=f, kFonly=True)
xx,yy = Occ(f=f)
ax.plot(xx, yy, color=NiceColour("Orange"), dashes=(2,1), lw=3)
for K, (Lbl,Col) in enumerate([("unpolarized", "Teal"),
("polarized", "Navy"),
("cofe", "Orange"),
]):
AddBorder(
ax.text(0.12+K*0.25, 0.1, Lbl, color=NiceColour(Col),
horizontalalignment="center",
fontsize=14, transform=ax.transAxes)
)
ax.axis([0, 1.3*Get_kf(), 0., 2.1])
ax.set_xticks([kfu, kfd, kf, kff],
['$k_F^{\\uparrow}$', '$k_F^{\\downarrow}$',
'$k_F$', '$\\bar{k}_F^{\\rm cofe}$'])
ax.set_yticks([0,0.5,1,1.5,2.])
ax.set_yticklabels(['0', '', '$\\uparrow$',
'', '$\\uparrow\\!\\!\\downarrow$'])
ax.set_xlabel("Wavenumber, $q$", fontsize=14)
ax.set_ylabel("Occ., $f_q$", fontsize=14)
plt.tight_layout(pad=0.3)
plt.savefig("FigOccs.pdf")
if ShowMultiOccs:
fig, axs = plt.subplots(4, 1, figsize=(6,3), sharex=True)
#Gx_x = np.array([-0.5, -0.6, -0.8, -1.0])
#zeta_x = np.sqrt(-1-2*Gx_x)
zeta_x = [0, 0.34, 0.66, 1.]
for zeta, ax in zip(zeta_x,axs):
f, Gx = zeta_to_f(zeta)
#Gx = -(1+zeta**2)/2
#f = 2*Gx/(3*Gx+1)
print("zeta = %.3f, Gx = %.3f, f = %.3f"%(zeta, Gx, f))
xx,yy = Occ(zeta=zeta)
ax.plot(xx, yy, color=NiceColour("Navy"), lw=3)
xx,yy = Occ(f=f)
ax.plot(xx, yy, color=NiceColour("Orange"), dashes=(2,1), lw=3)
XLbl, YLbl, InterpLbl = 0.77, 0.97, "$G_{\\rm x}=%.2f$"%(Gx)
XLbl, YLbl, InterpLbl = 0.02, 0.47, "$\zeta=%.2f$, $\\bar{f}=%.2f$"\
%(zeta, f)
AddBorder(
ax.text(XLbl, YLbl, InterpLbl,
verticalalignment="top",
fontsize=14,
transform=ax.transAxes,
)
)
if ax==axs[3]:
for K, (Lbl,Col) in enumerate([
("polarized gas", "Navy"),
("cofe gas", "Orange"),
]):
AddBorder(
ax.text(0.55+K*0.25, 0.95, Lbl, color=NiceColour(Col),
horizontalalignment="center",
verticalalignment="top",
fontsize=14, transform=ax.transAxes)
)
ax.axis([0, Range*Get_kf(), -0.1, 2.1])
ax.set_xticks([])
ax.set_yticks([0,0.5,1,1.5,2.])
ax.set_yticklabels(['0','','1','','2'])
#ax.set_yticklabels(['0', '', '$\\uparrow$',
# '', '$\\uparrow\\!\\!\\!\\!\\downarrow$'])
ax.set_xlabel("Wavenumber, $q$", fontsize=14)
fig.supylabel("Occupation factor, $f_q$", fontsize=14)
plt.subplots_adjust(hspace=0.)
plt.tight_layout(pad=0.3, h_pad=0.0, w_pad=0.0)
plt.savefig("FigMultiOccs.pdf")
if ShowEnhance:
fig, ax = plt.subplots(1, 1, figsize=(6,2))
zeta = np.linspace(0, 1, 81)
Gx = -(1+zeta**2)/2
f = 2*Gx/(3*Gx+1)
Fpol = ((1+zeta)**(4/3) + (1-zeta)**(4/3))/2.
Fcofe = (3. + 1./Gx)**(1/3)
Fldpol = 1.96 - Fpol
Fldcofe = 1.96 - Fcofe
Fhdpol = IWP91(zeta)# From WP91
Fhdcofe = f/2.
def Xi(F,x=None):
if x is None:
return (F-F[0])/(F[-1]-F[0])
else:
return np.interp(x, zeta, Xi(F))
ax.plot(zeta, Xi(Fpol),
color=NiceColour("Navy"),
label="x/c(ld)",
)
ax.plot(zeta, Xi(Fhdpol), dashes=(2,1),
color=NiceColour("Navy"),
label="c(hd)",
)
ax.text(0.6, Xi(Fhdpol, 0.6)-0.1, "pol",
color=NiceColour("Navy"), fontsize=14,
)
ax.plot(zeta, Xi(Fcofe),
color=NiceColour("Orange"),
)
ax.plot(zeta, Xi(Fhdcofe), dashes=(2,1),
color=NiceColour("Orange"),
)
ax.text(0.4, Xi(Fhdcofe, 0.4)+0.1, "cofe",
color=NiceColour("Orange"), fontsize=14,
)
ax.legend(loc="upper left")
ax.axis([0, 1, -0.01, 1.01])
ax.set_xticks([0,0.5,1])
ax.set_xticklabels(['$0$','$\\frac{1}{2}$', '$1$'])
ax.set_xlabel("Effective polarization, $\\zeta$", fontsize=14)
ax.set_ylabel("Enhancement", fontsize=14)
plt.tight_layout(pad=0.3)
plt.show()