diff --git a/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems.py b/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems.py index 8e69235..bdd7b0d 100755 --- a/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems.py +++ b/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems.py @@ -9,29 +9,29 @@ import copy import time -def lead_matrix_00(y): - h00 = np.zeros((y, y)) - for y0 in range(y-1): - h00[y0, y0+1] = 1 - h00[y0+1, y0] = 1 +def get_lead_h00(width): + h00 = np.zeros((width, width)) + for i0 in range(width-1): + h00[i0, i0+1] = 1 + h00[i0+1, i0] = 1 return h00 -def lead_matrix_01(y): - h01 = np.identity(y) +def get_lead_h01(width): + h01 = np.identity(width) return h01 -def scattering_region(x, y): - h = np.zeros((x*y, x*y)) - for x0 in range(x-1): - for y0 in range(y): - h[x0*y+y0, (x0+1)*y+y0] = 1 # x方向的跃迁 - h[(x0+1)*y+y0, x0*y+y0] = 1 - for x0 in range(x): - for y0 in range(y-1): - h[x0*y+y0, x0*y+y0+1] = 1 # y方向的跃迁 - h[x0*y+y0+1, x0*y+y0] = 1 +def get_center_hamiltonian(Nx, Ny): + h = np.zeros((Nx*Ny, Nx*Ny)) + for x0 in range(Nx-1): + for y0 in range(Ny): + h[x0*Ny+y0, (x0+1)*Ny+y0] = 1 # x方向的跃迁 + h[(x0+1)*Ny+y0, x0*Ny+y0] = 1 + for x0 in range(Nx): + for y0 in range(Ny-1): + h[x0*Ny+y0, x0*Ny+y0+1] = 1 # y方向的跃迁 + h[x0*Ny+y0+1, x0*Ny+y0] = 1 return h @@ -42,11 +42,11 @@ def main(): fermi_energy_array = np.arange(-4, 4, .01) # 中心区的哈密顿量 - H_scattering_region = scattering_region(x=length, y=width) + H_center = get_center_hamiltonian(Nx=length, Ny=width) # 电极的h00和h01 - lead_h00 = lead_matrix_00(width) - lead_h01 = lead_matrix_01(width) + lead_h00 = get_lead_h00(width) + lead_h01 = get_lead_h01(width) transmission_12_array = [] transmission_13_array = [] @@ -74,31 +74,31 @@ def main(): # lead6 lead5 # 电极到中心区的跃迁矩阵 - H_from_lead_1_to_center = np.zeros((width, width*length), dtype=complex) - H_from_lead_2_to_center = np.zeros((width, width*length), dtype=complex) - H_from_lead_3_to_center = np.zeros((width, width*length), dtype=complex) - H_from_lead_4_to_center = np.zeros((width, width*length), dtype=complex) - H_from_lead_5_to_center = np.zeros((width, width*length), dtype=complex) - H_from_lead_6_to_center = np.zeros((width, width*length), dtype=complex) + H_lead_1_to_center = np.zeros((width, width*length), dtype=complex) + H_lead_2_to_center = np.zeros((width, width*length), dtype=complex) + H_lead_3_to_center = np.zeros((width, width*length), dtype=complex) + H_lead_4_to_center = np.zeros((width, width*length), dtype=complex) + H_lead_5_to_center = np.zeros((width, width*length), dtype=complex) + H_lead_6_to_center = np.zeros((width, width*length), dtype=complex) move = 0 # the step of leads 2,3,6,5 moving to center for i0 in range(width): - H_from_lead_1_to_center[i0, i0] = 1 - H_from_lead_2_to_center[i0, width*(move+i0)+(width-1)] = 1 - H_from_lead_3_to_center[i0, width*(length-move-1-i0)+(width-1)] = 1 - H_from_lead_4_to_center[i0, width*(length-1)+i0] = 1 - H_from_lead_5_to_center[i0, width*(length-move-1-i0)+0] = 1 - H_from_lead_6_to_center[i0, width*(move+i0)+0] = 1 + H_lead_1_to_center[i0, i0] = 1 + H_lead_2_to_center[i0, width*(move+i0)+(width-1)] = 1 + H_lead_3_to_center[i0, width*(length-move-1-i0)+(width-1)] = 1 + H_lead_4_to_center[i0, width*(length-1)+i0] = 1 + H_lead_5_to_center[i0, width*(length-move-1-i0)+0] = 1 + H_lead_6_to_center[i0, width*(move+i0)+0] = 1 # 自能 - self_energy_1 = np.dot(np.dot(H_from_lead_1_to_center.transpose().conj(), lead_1), H_from_lead_1_to_center) - self_energy_2 = np.dot(np.dot(H_from_lead_2_to_center.transpose().conj(), lead_2), H_from_lead_2_to_center) - self_energy_3 = np.dot(np.dot(H_from_lead_3_to_center.transpose().conj(), lead_3), H_from_lead_3_to_center) - self_energy_4 = np.dot(np.dot(H_from_lead_4_to_center.transpose().conj(), lead_4), H_from_lead_4_to_center) - self_energy_5 = np.dot(np.dot(H_from_lead_5_to_center.transpose().conj(), lead_5), H_from_lead_5_to_center) - self_energy_6 = np.dot(np.dot(H_from_lead_6_to_center.transpose().conj(), lead_6), H_from_lead_6_to_center) + self_energy_1 = np.dot(np.dot(H_lead_1_to_center.transpose().conj(), lead_1), H_lead_1_to_center) + self_energy_2 = np.dot(np.dot(H_lead_2_to_center.transpose().conj(), lead_2), H_lead_2_to_center) + self_energy_3 = np.dot(np.dot(H_lead_3_to_center.transpose().conj(), lead_3), H_lead_3_to_center) + self_energy_4 = np.dot(np.dot(H_lead_4_to_center.transpose().conj(), lead_4), H_lead_4_to_center) + self_energy_5 = np.dot(np.dot(H_lead_5_to_center.transpose().conj(), lead_5), H_lead_5_to_center) + self_energy_6 = np.dot(np.dot(H_lead_6_to_center.transpose().conj(), lead_6), H_lead_6_to_center) # 整体格林函数 - green = np.linalg.inv(fermi_energy*np.eye(width*length)-H_scattering_region-self_energy_1-self_energy_2-self_energy_3-self_energy_4-self_energy_5-self_energy_6) + green = np.linalg.inv(fermi_energy*np.eye(width*length)-H_center-self_energy_1-self_energy_2-self_energy_3-self_energy_4-self_energy_5-self_energy_6) # Gamma矩阵 gamma_1 = 1j*(self_energy_1-self_energy_1.transpose().conj()) diff --git a/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems_with_guan.py b/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems_with_guan.py index bdb52b3..72303fa 100644 --- a/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems_with_guan.py +++ b/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems_with_guan.py @@ -7,29 +7,29 @@ import numpy as np import time import guan -def lead_matrix_00(y): - h00 = np.zeros((y, y)) - for y0 in range(y-1): - h00[y0, y0+1] = 1 - h00[y0+1, y0] = 1 +def get_lead_h00(width): + h00 = np.zeros((width, width)) + for i0 in range(width-1): + h00[i0, i0+1] = 1 + h00[i0+1, i0] = 1 return h00 -def lead_matrix_01(y): - h01 = np.identity(y) +def get_lead_h01(width): + h01 = np.identity(width) return h01 -def scattering_region(x, y): - h = np.zeros((x*y, x*y)) - for x0 in range(x-1): - for y0 in range(y): - h[x0*y+y0, (x0+1)*y+y0] = 1 # x方向的跃迁 - h[(x0+1)*y+y0, x0*y+y0] = 1 - for x0 in range(x): - for y0 in range(y-1): - h[x0*y+y0, x0*y+y0+1] = 1 # y方向的跃迁 - h[x0*y+y0+1, x0*y+y0] = 1 +def get_center_hamiltonian(Nx, Ny): + h = np.zeros((Nx*Ny, Nx*Ny)) + for x0 in range(Nx-1): + for y0 in range(Ny): + h[x0*Ny+y0, (x0+1)*Ny+y0] = 1 # x方向的跃迁 + h[(x0+1)*Ny+y0, x0*Ny+y0] = 1 + for x0 in range(Nx): + for y0 in range(Ny-1): + h[x0*Ny+y0, x0*Ny+y0+1] = 1 # y方向的跃迁 + h[x0*Ny+y0+1, x0*Ny+y0] = 1 return h @@ -40,11 +40,11 @@ def main(): fermi_energy_array = np.arange(-4, 4, .01) # 中心区的哈密顿量 - H_scattering_region = scattering_region(x=length, y=width) + H_center = get_center_hamiltonian(Nx=length, Ny=width) # 电极的h00和h01 - lead_h00 = lead_matrix_00(width) - lead_h01 = lead_matrix_01(width) + lead_h00 = get_lead_h00(width) + lead_h01 = get_lead_h01(width) transmission_12_array = [] transmission_13_array = [] @@ -84,7 +84,7 @@ def main(): self_energy6, gamma6 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, lead_h00, lead_h01, h_lead6_to_center) # 整体格林函数 - green = np.linalg.inv(fermi_energy*np.eye(width*length)-H_scattering_region-self_energy1-self_energy2-self_energy3-self_energy4-self_energy5-self_energy6) + green = np.linalg.inv(fermi_energy*np.eye(width*length)-H_center-self_energy1-self_energy2-self_energy3-self_energy4-self_energy5-self_energy6) # Transmission transmission_12 = np.trace(np.dot(np.dot(np.dot(gamma1, green), gamma2), green.transpose().conj()))