def GammaDLT0(t, kappa, Omega, diff=0):
'''
The decoherence function of the Drude-Lorentz cutoff for T = 0.
See Eq.(A9) of Sato J.Chem.Phys.150(2019)224108
diff = 0 : the order of differentiation with respect to time
'''
cosh = np.cosh(Omega * t)
sinh = np.sinh(Omega * t)
# Note: Shi(z) = shici(z)[0] and Chi(z) = shici(z)[1]
Shi = shichi(Omega * t)[0]
Chi = shichi(Omega * t)[1]
if diff == 0:
val = sinh * Shi - cosh * Chi
val += EulerGamma + np.log(Omega * t)
return kappa * val
elif diff == 1:
val = cosh * Shi - sinh * Chi
return kappa * Omega * val
elif diff == 2:
val = sinh * Shi - cosh * Chi
return kappa * Omega**2 * val
else:
return 0
def test_shichi_consistency():
# Make sure the implementation of shichi for real arguments agrees
# with the implementation of shichi for complex arguments.
# On the negative real axis Cephes drops the imaginary part in chi
def shichi(x):
shi, chi = sc.shichi(x + 0j)
return shi.real, chi.real
# Overflow happens quickly, so limit range
x = np.r_[-np.logspace(np.log10(700), -30, 200), 0, np.logspace(-30, 2, np.log10(700))]
shi, chi = sc.shichi(x)
dataset = np.column_stack((x, shi, chi))
FuncData(shichi, dataset, 0, (1, 2), rtol=1e-14).check()
def test_shichi_consistency():
# Make sure the implementation of shichi for real arguments agrees
# with the implementation of shichi for complex arguments.
# On the negative real axis Cephes drops the imaginary part in chi
def shichi(x):
shi, chi = sc.shichi(x + 0j)
return shi.real, chi.real
# Overflow happens quickly, so limit range
x = np.r_[-np.logspace(np.log10(700), -30, 200), 0,
np.logspace(-30, np.log10(700), 200)]
shi, chi = sc.shichi(x)
dataset = np.column_stack((x, shi, chi))
FuncData(shichi, dataset, 0, (1, 2), rtol=1e-14).check()
def exparg(h, k=k1, tb=tbath):
"""
Argument of the exponentials in the solution of the MCE equation where the magnetic field dependence of the heat capacity C is taken into account.
See Wolfram alpha for a human readable version of the solution of the equation
Parameters
----------
h : array
Reduced magnetic field H/Hc0.
k : scalar, optional
Prefactor of the second term in the RHS of the equation. The default is k1.
tb : scalar, optional
Reduced bath temperature Tbat/Tc0. The default is tbath.
Returns
-------
y : array
Final computed quantity.
"""
y = - k * tb * shichi(2*h/tb)[0] + \
k * tb**2 / (2*h) * (1 + np.cosh(2*h/tb))
return y
def shichi(x):
shi, chi = sc.shichi(x + 0j)
return shi.real, chi.real
def chi(x):
return sc.shichi(x)[1]
def shi(x):
return sc.shichi(x)[0]
def chi(x):
return sc.shichi(x)[1]
def shi(x):
return sc.shichi(x)[0]
def shichi(x):
shi, chi = sc.shichi(x + 0j)
return shi.real, chi.real
#add EAGT 12 gsl functions eagt_12f_name=['gsl_airy_ai','gsl_sf_Chi','gsl_sf_Ci','gsl_sf_bessel_J0','gsl_sf_bessel_J1','gsl_sf_bessel_Y0','gsl_sf_bessel_Y1','gsl_sf_eta','gsl_sf_gamma','gsl_sf_legendre_P2','gsl_sf_legendre_P3','gsl_sf_lngamma'] eagt_12f_tmpn=['gsl_airy_ai','gsl_sf_bessel_Y1','gsl_sf_bessel_Y0','gsl_sf_bessel_J1','gsl_sf_bessel_J0','gsl_sf_Chi','gsl_sf_gamma','gsl_sf_Ci','gsl_sf_lngamma','gsl_sf_legendre_P2','gsl_sf_legendre_P3'] gsl_airy_ai = lambda t: sf.airy_Ai(t, 0) bessely1 = lambda t: bessely(1, t) bessely0 = lambda t: bessely(0, t) besselj1 = lambda t: besselj(1, t) besselj0 = lambda t: besselj(0, t) legendre3 = lambda t: legendre(3, t) legendre2 = lambda t: legendre(2, t) pyairyai = lambda z: sc.airy(z)[0] pybessely1 = sc.y1 pybessely0 = sc.y0 pybesselj1 = sc.j1 pybesselj0 = sc.j0 pychi = lambda z: sc.shichi(z)[1] pyeta = lambda x: (1.0-math.pow(2.0,1.0-x))*sc.zeta(x,1) pygamma = sc.gamma pyci = lambda z:sc.sici(z)[1] pyloggamma = lambda z: (sc.loggamma(z)).real pylegendre3 = lambda x: sc.eval_legendre(3, x) pylegendre2 = lambda x: sc.eval_legendre(2, x) rf_12_l = [airyai,bessely1,bessely0,besselj1,besselj0,chi,altzeta,gamma,ci,loggamma,legendre3,legendre2] gf_12_l = [gsl_airy_ai,sf.bessel_Y1,sf.bessel_Y0,sf.bessel_J1,sf.bessel_J0,sf.Chi,sf.eta,sf.gamma,sf.Ci,sf.lngamma,sf.legendre_P3,sf.legendre_P2] pf_12_l = [pyairyai,pybessely1,pybessely0,pybesselj1,pybesselj0,pychi,pyeta,pygamma,pyci,pyloggamma,pylegendre3,pylegendre2] input_domain_12 = [[[-823549.6645, 102]],[[1.0, 1.7e10]],[[1.0, 1.7e10]],[[0, 1.7e+100]],[[0, 1.7e+100]],[[0, 700]],[[-168, 100]],[[-168, 168]],[[1.0, 823549]],[[0.0, 1000.0]],[[-1.7976931348623157e+10, 1.7976931348623157e+10]],[[-1.7976931348623157e+10, 1.7976931348623157e+10]]] input_domain_12_py = [[[-823549.6645, 102]],[[1.0, 1.7e10]],[[1.0, 1.7e10]],[[0, 1.7e+100]],[[0, 1.7e+100]],[[0, 700]],[[1, 100]],[[0, 168]],[[1.0, 823549]],[[0.0, 1000.0]],[[-1.7976931348623157e+10, 1.7976931348623157e+10]],[[-1.7976931348623157e+10, 1.7976931348623157e+10]]] # The iteration number n_r_iter = 20 mp.pre = 200 x = 1.2414480316687057e+40