0.1.13
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204
PyPI/src/guan/band_structures_and_wave_functions.py
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204
PyPI/src/guan/band_structures_and_wave_functions.py
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# Module: band_structures_and_wave_functions
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# 计算哈密顿量的本征值
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def calculate_eigenvalue(hamiltonian):
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import numpy as np
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if np.array(hamiltonian).shape==():
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eigenvalue = np.real(hamiltonian)
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else:
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eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
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import guan
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guan.statistics_of_guan_package()
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return eigenvalue
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# 输入哈密顿量函数（带一组参数），计算一组参数下的本征值，返回本征值向量组
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def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print_show=0):
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import numpy as np
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dim_x = np.array(x_array).shape[0]
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i0 = 0
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if np.array(hamiltonian_function(0)).shape==():
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eigenvalue_array = np.zeros((dim_x, 1))
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for x0 in x_array:
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hamiltonian = hamiltonian_function(x0)
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eigenvalue_array[i0, 0] = np.real(hamiltonian)
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i0 += 1
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else:
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dim = np.array(hamiltonian_function(0)).shape[0]
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eigenvalue_array = np.zeros((dim_x, dim))
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for x0 in x_array:
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if print_show==1:
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print(x0)
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hamiltonian = hamiltonian_function(x0)
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eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
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eigenvalue_array[i0, :] = eigenvalue
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i0 += 1
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import guan
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guan.statistics_of_guan_package()
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return eigenvalue_array
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# 输入哈密顿量函数（带两组参数），计算两组参数下的本征值，返回本征值向量组
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def calculate_eigenvalue_with_two_parameters(x_array, y_array, hamiltonian_function, print_show=0, print_show_more=0):
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import numpy as np
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dim_x = np.array(x_array).shape[0]
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dim_y = np.array(y_array).shape[0]
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if np.array(hamiltonian_function(0,0)).shape==():
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eigenvalue_array = np.zeros((dim_y, dim_x, 1))
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i0 = 0
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for y0 in y_array:
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j0 = 0
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for x0 in x_array:
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hamiltonian = hamiltonian_function(x0, y0)
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eigenvalue_array[i0, j0, 0] = np.real(hamiltonian)
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j0 += 1
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i0 += 1
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else:
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dim = np.array(hamiltonian_function(0, 0)).shape[0]
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eigenvalue_array = np.zeros((dim_y, dim_x, dim))
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i0 = 0
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for y0 in y_array:
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j0 = 0
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if print_show==1:
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print(y0)
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for x0 in x_array:
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if print_show_more==1:
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print(x0)
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hamiltonian = hamiltonian_function(x0, y0)
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eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
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eigenvalue_array[i0, j0, :] = eigenvalue
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j0 += 1
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i0 += 1
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import guan
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guan.statistics_of_guan_package()
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return eigenvalue_array
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# 计算哈密顿量的本征矢
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def calculate_eigenvector(hamiltonian):
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import numpy as np
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eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
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import guan
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guan.statistics_of_guan_package()
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return eigenvector
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# 通过二分查找的方法获取和相邻波函数一样规范的波函数
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def find_vector_with_the_same_gauge_with_binary_search(vector_target, vector_ref, show_error=1, show_times=0, show_phase=0, n_test=1000, precision=1e-6):
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import numpy as np
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import cmath
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phase_1_pre = 0
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phase_2_pre = np.pi
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for i0 in range(n_test):
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test_1 = np.sum(np.abs(vector_target*cmath.exp(1j*phase_1_pre) - vector_ref))
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test_2 = np.sum(np.abs(vector_target*cmath.exp(1j*phase_2_pre) - vector_ref))
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if test_1 < precision:
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phase = phase_1_pre
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if show_times==1:
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print('Binary search times=', i0)
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break
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if i0 == n_test-1:
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phase = phase_1_pre
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if show_error==1:
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print('Gauge not found with binary search times=', i0)
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if test_1 < test_2:
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if i0 == 0:
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phase_1 = phase_1_pre-(phase_2_pre-phase_1_pre)/2
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phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2
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else:
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phase_1 = phase_1_pre
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phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2
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else:
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if i0 == 0:
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phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2
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phase_2 = phase_2_pre+(phase_2_pre-phase_1_pre)/2
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else:
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phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2
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phase_2 = phase_2_pre
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phase_1_pre = phase_1
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phase_2_pre = phase_2
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vector_target = vector_target*cmath.exp(1j*phase)
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if show_phase==1:
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print('Phase=', phase)
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import guan
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guan.statistics_of_guan_package()
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return vector_target
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# 通过使得波函数的一个非零分量为实数，得到固定规范的波函数
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def find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.005, index=None):
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import numpy as np
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import cmath
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vector = np.array(vector)
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if index == None:
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index = np.argmax(np.abs(vector))
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sign_pre = np.sign(np.imag(vector[index]))
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for phase in np.arange(0, 2*np.pi, precision):
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sign = np.sign(np.imag(vector[index]*cmath.exp(1j*phase)))
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if np.abs(np.imag(vector[index]*cmath.exp(1j*phase))) < 1e-9 or sign == -sign_pre:
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break
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sign_pre = sign
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vector = vector*cmath.exp(1j*phase)
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if np.real(vector[index]) < 0:
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vector = -vector
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import guan
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guan.statistics_of_guan_package()
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return vector
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# 通过使得波函数的一个非零分量为实数，得到固定规范的波函数（在一组波函数中选取最大的那个分量）
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def find_vector_array_with_fixed_gauge_by_making_one_component_real(vector_array, precision=0.005):
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import numpy as np
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import guan
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vector_sum = 0
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Num_k = np.array(vector_array).shape[0]
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for i0 in range(Num_k):
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vector_sum += np.abs(vector_array[i0])
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index = np.argmax(np.abs(vector_sum))
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for i0 in range(Num_k):
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vector_array[i0] = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector_array[i0], precision=precision, index=index)
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guan.statistics_of_guan_package()
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return vector_array
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# 旋转两个简并的波函数（说明：参数比较多，效率不高）
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def rotation_of_degenerate_vectors(vector1, vector2, index1=None, index2=None, precision=0.01, criterion=0.01, show_theta=0):
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import numpy as np
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import math
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import cmath
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vector1 = np.array(vector1)
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vector2 = np.array(vector2)
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if index1 == None:
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index1 = np.argmax(np.abs(vector1))
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if index2 == None:
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index2 = np.argmax(np.abs(vector2))
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if np.abs(vector1[index2])>criterion or np.abs(vector2[index1])>criterion:
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for theta in np.arange(0, 2*math.pi, precision):
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if show_theta==1:
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print(theta)
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for phi1 in np.arange(0, 2*math.pi, precision):
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for phi2 in np.arange(0, 2*math.pi, precision):
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vector1_test = cmath.exp(1j*phi1)*vector1*math.cos(theta)+cmath.exp(1j*phi2)*vector2*math.sin(theta)
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vector2_test = -cmath.exp(-1j*phi2)*vector1*math.sin(theta)+cmath.exp(-1j*phi1)*vector2*math.cos(theta)
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if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
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vector1 = vector1_test
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vector2 = vector2_test
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break
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if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
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break
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if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
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break
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import guan
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guan.statistics_of_guan_package()
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return vector1, vector2
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# 旋转两个简并的波函数向量组（说明：参数比较多，效率不高）
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def rotation_of_degenerate_vectors_array(vector1_array, vector2_array, precision=0.01, criterion=0.01, show_theta=0):
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import numpy as np
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import guan
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Num_k = np.array(vector1_array).shape[0]
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vector1_sum = 0
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for i0 in range(Num_k):
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vector1_sum += np.abs(vector1_array[i0])
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index1 = np.argmax(np.abs(vector1_sum))
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vector2_sum = 0
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for i0 in range(Num_k):
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vector2_sum += np.abs(vector2_array[i0])
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index2 = np.argmax(np.abs(vector2_sum))
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for i0 in range(Num_k):
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vector1_array[i0], vector2_array[i0] = guan.rotation_of_degenerate_vectors(vector1=vector1_array[i0], vector2=vector2_array[i0], index1=index1, index2=index2, precision=precision, criterion=criterion, show_theta=show_theta)
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guan.statistics_of_guan_package()
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return vector1_array, vector2_array
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