gftool.lattice.bethe.gf_ret_t
- gftool.lattice.bethe.gf_ret_t(tt, half_bandwidth, center=0)[source]
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()