gftool.lattice.bethe.gf_ret_t

gftool.lattice.bethe.gf_ret_t(tt, half_bandwidth, center=0)

Retarded-time local Green’s function of Bethe lattice with Z=∞.

\[G(t) = -2j * Θ(t) * J_1(Dt)/(Dt)\]

where \(D\) is the half bandwidth and \(J_1(t)\) is the Bessel function of first kind.

Parameters:

ttfloat array_like or float

Green’s function is evaluated at time tt.

half_bandwidthfloat

Half-bandwidth of the DOS of the Bethe lattice. The half_bandwidth corresponds to the nearest neighbor hopping t=D/2.

centerfloat

Position of the center of the Bethe DOS. This parameter is not given in units of half_bandwidth.

Returns:

complex np.ndarray or complex

Value of the retarded-time Bethe Green’s function.

Examples

>>> tt = np.linspace(0, 50, 1500)
>>> gf_tt = gt.lattice.bethe.gf_ret_t(tt, half_bandwidth=1)

>>> import matplotlib.pyplot as plt
>>> _ = plt.axhline(0, color='black', linewidth=0.8)
>>> _ = plt.plot(tt, gf_tt.real, label=r"$\Re G$")
>>> _ = plt.plot(tt, gf_tt.imag, '--', label=r"$\Im G$")
>>> _ = plt.xlabel(r"$t*D$")
>>> _ = plt.ylabel(r"$G$")
>>> _ = plt.xlim(left=tt.min(), right=tt.max())
>>> _ = plt.legend()
>>> plt.show()

(png, pdf)