import sys import os sys.path.append('../code') from init_mooc_nb import * init_notebook() # Set the path to a folder containing data files, to work with filters as well. data_folder = 'data/' if os.path.exists('data') and os.path.isdir('data') else '../data/' MoocVideo("sbbyL0RDH-o", src_location="9.1-intro") question = "How is the flow in the diagram above altered if we stack 10 1D systems next to each other and weakly couple them?" answers = ["Nothing changes.", r"$\beta$ is multiplied by 10.", "The scaling hypothesis doesn't apply since we don't have a 1D system anymore.", r"$\beta$ is altered in some way, since we have a different disordered system now."] explanation = "The scaling hypothesis tells us that the details of the Hamiltonian don't matter, so the scaling flow stays the same." MoocMultipleChoiceAssessment(question=question, answers=answers, correct_answer=0, explanation=explanation) data = np.loadtxt(data_folder + 'data_from_doru.dat') fig, ax = plt.subplots(figsize=(6, 4)) cmap = plt.get_cmap('gist_heat') for i in range(3): x, y = data[i::3, 0], data[i::3, 2] error = data[i::3, 3] L = data[i, 1] color = cmap(np.log(L-26)/np.log(243-26) * .7) ax.errorbar(x, y, yerr=error, label="$L=%i$" % L, color=color) plt.legend() plt.xlabel('$V$') plt.ylabel(r'$\langle G \rangle$') evals = [5.5, 5.75, 6] ax.set_xticks(evals) ax.set_xticklabels(["${0}$".format(i) for i in evals]) evals = [1, 1.5, 2] ax.set_yticks(evals) ax.set_yticklabels(["${0}$".format(i) for i in evals]) ax.set_xlim(5.5, 6.0) ax.set_ylim(1.0, 2.0) plt.show() question = r"What would we see if $\beta$ crossed from positive to negative values?" answers = ["Small conductances would have a metallic phase, where $g$ grows indefinitely, " "while large $g$ would lead to an insulator.", "We would see a critical phase, where all conductances converge to the same value.", r"This is just the same metal-insulator transition since $\beta(g_c) = 0$", "This is an impossible scaling function."] explanation = ("Both larger conductances and smaller conductances flow towards the critical value, " "so all systems get the same conductance when their size becomes large enough. " "This is an attractive critical point.") MoocMultipleChoiceAssessment(question=question, answers=answers, correct_answer=1, explanation=explanation) MoocVideo("JdDeBJEBO0s", src_location="9.1-summary") MoocDiscussion("Questions", "Anderson localization")