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593 | 593 | </li> |
594 | 594 |
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595 | 595 | <li class="md-nav__item"> |
596 | | - <a href="#example-problem-calculate-chern-numbers-for-the-haldane-model" class="md-nav__link"> |
| 596 | + <a href="#example-calculate-chern-numbers-for-the-haldane-model" class="md-nav__link"> |
597 | 597 | <span class="md-ellipsis"> |
598 | | - Example Problem: Calculate Chern numbers for the Haldane Model |
| 598 | + Example: Calculate Chern numbers for the Haldane Model |
599 | 599 | </span> |
600 | 600 | </a> |
601 | 601 |
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602 | | - <nav class="md-nav" aria-label="Example Problem: Calculate Chern numbers for the Haldane Model"> |
| 602 | + <nav class="md-nav" aria-label="Example: Calculate Chern numbers for the Haldane Model"> |
603 | 603 | <ul class="md-nav__list"> |
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1016 | 1016 | </li> |
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1019 | | - <a href="#example-problem-calculate-chern-numbers-for-the-haldane-model" class="md-nav__link"> |
| 1019 | + <a href="#example-calculate-chern-numbers-for-the-haldane-model" class="md-nav__link"> |
1020 | 1020 | <span class="md-ellipsis"> |
1021 | | - Example Problem: Calculate Chern numbers for the Haldane Model |
| 1021 | + Example: Calculate Chern numbers for the Haldane Model |
1022 | 1022 | </span> |
1023 | 1023 | </a> |
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1025 | | - <nav class="md-nav" aria-label="Example Problem: Calculate Chern numbers for the Haldane Model"> |
| 1025 | + <nav class="md-nav" aria-label="Example: Calculate Chern numbers for the Haldane Model"> |
1026 | 1026 | <ul class="md-nav__list"> |
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@@ -1168,102 +1168,101 @@ <h2 id="benchmark-statistics">Benchmark Statistics</h2> |
1168 | 1168 | </table> |
1169 | 1169 | <p>Nobel prized related problems:</p> |
1170 | 1170 | <h3 id="numerical-linear-algebra">Numerical Linear Algebra</h3> |
1171 | | -<p>1. |
1172 | | -2. |
1173 | | -3. |
1174 | | -4. |
1175 | | -5. |
1176 | | -6. |
1177 | | -7.</p> |
| 1171 | +<p>1_CG |
| 1172 | +3_Gauss_Seidel |
| 1173 | +4_IncomChol |
| 1174 | +5_Lanczos |
| 1175 | +9_Weighted_Jacobi |
| 1176 | +29_Gram_Schmidt_orthogonalization |
| 1177 | +31_independent_component_analysis |
| 1178 | +74_Householder_QR</p> |
1178 | 1179 | <h3 id="computational-mechanics">Computational Mechanics</h3> |
1179 | | -<p>1. |
1180 | | -2. |
1181 | | -3. |
1182 | | -4. |
1183 | | -5. |
1184 | | -6.</p> |
| 1180 | +<p>18_NURBS |
| 1181 | +24_Burgers_equation |
| 1182 | +40_Spliting_Operator |
| 1183 | +54_SUPG |
| 1184 | +78_Chaotic_Dynamics_Pendulum</p> |
1185 | 1185 | <h3 id="computational-finance">Computational Finance</h3> |
1186 | | -<p>1.</p> |
| 1186 | +<p>63_Estimating_Stock_Option_Price</p> |
1187 | 1187 | <h3 id="condensed-matter-physics">Condensed Matter Physics</h3> |
1188 | | -<p>1. |
1189 | | -2. |
1190 | | -3. |
1191 | | -4. |
1192 | | -5. |
1193 | | -6. |
1194 | | -7. |
1195 | | -8. |
1196 | | -9. |
1197 | | -10. |
1198 | | -11. |
1199 | | -12. |
1200 | | -13.</p> |
| 1188 | +<p>17_linear_tetrahedron_method |
| 1189 | +20_phonon_angular_momentum |
| 1190 | +33_phase_diagram_chern_haldane_model |
| 1191 | +38_Reciprocal_lattice_vector |
| 1192 | +48_MEELS_conversion |
| 1193 | +50_Replica_symmetry_breaking |
| 1194 | +62_dmrg |
| 1195 | +67_LEG_Dyson_equation_bulk |
| 1196 | +69_LEG_Dyson_equation_semi_infinite |
| 1197 | +72_ising_model |
| 1198 | +73_Xray_conversion_II |
| 1199 | +75_graphene_tight_binding</p> |
1201 | 1200 | <h3 id="optics">Optics</h3> |
1202 | | -<p>1. |
1203 | | -2. |
1204 | | -3. |
1205 | | -4. |
1206 | | -5. |
1207 | | -6. |
1208 | | -7. |
1209 | | -8. |
1210 | | -9. |
1211 | | -10.</p> |
| 1201 | +<p>2_Gaussian_Beam_Focus |
| 1202 | +6_Spatial_filters_I |
| 1203 | +7_Spatial_filters_II |
| 1204 | +8_Spatial_filters_III |
| 1205 | +14_Brownian_motion_in_the_optical_tweezer |
| 1206 | +22_Beam_translation_reexpansion |
| 1207 | +28_Gaussian_Beam_Intensity |
| 1208 | +32_Multiparticle_dynamics_in_the_optical_tweezer_array |
| 1209 | +37_ray_optics_spherical_aberration |
| 1210 | +43_two_end_fiber_laser_generator</p> |
1212 | 1211 | <h3 id="quantum-informationcomputing">Quantum Information/Computing</h3> |
1213 | | -<p>1. |
1214 | | -2. |
1215 | | -3. |
1216 | | -4. |
1217 | | -5. |
1218 | | -6.</p> |
| 1212 | +<p>11_GADC_entanglement |
| 1213 | +19_n_tangle |
| 1214 | +23_Blahut_Arimoto |
| 1215 | +59_VQE |
| 1216 | +65_GHZ_protocol_fidelity |
| 1217 | +71_GADC_rev_coherent_info</p> |
1219 | 1218 | <h3 id="computational-physics">Computational Physics</h3> |
1220 | | -<p>1. |
1221 | | -2. |
1222 | | -3. |
1223 | | -4. |
1224 | | -5.</p> |
| 1219 | +<p>13_Maxwell_Equation_Solver |
| 1220 | +15_Crank_Nicolson_for_time_dependent_Schrodinger |
| 1221 | +45_finite_difference_heat_equation |
| 1222 | +52_Shooting_algo_H_atom |
| 1223 | +57_1D_harmonic_oscillator_numerov_shooting</p> |
1225 | 1224 | <h3 id="astrophysics">Astrophysics</h3> |
1226 | | -<p>1. |
1227 | | -2.</p> |
| 1225 | +<p>49_nbody |
| 1226 | +58_Tolman_Oppenheimer_Volkoff_star</p> |
1228 | 1227 | <h3 id="particle-physics">Particle Physics</h3> |
1229 | | -<p>1.</p> |
| 1228 | +<p>70_neutrino_oscillation</p> |
1230 | 1229 | <h3 id="quantum-chemistry">Quantum Chemistry</h3> |
1231 | | -<p>1. |
1232 | | -2. |
1233 | | -3. |
1234 | | -4. |
1235 | | -5.</p> |
| 1230 | +<p>12_Schrodinger_DFT_with_SCF |
| 1231 | +30_helium_slater_jastrow_wavefunction |
| 1232 | +46_helium_atom_vmc |
| 1233 | +66_kolmogorov_crespi_potential |
| 1234 | +68_helium_atom_dmc</p> |
1236 | 1235 | <h3 id="computational-chemistry">Computational Chemistry</h3> |
1237 | | -<p>1. |
1238 | | -2. |
1239 | | -3.</p> |
| 1236 | +<p>10_ewald_summation |
| 1237 | +16_Davidson_method |
| 1238 | +60_Widom_particle_insertion</p> |
1240 | 1239 | <h3 id="ecology">Ecology</h3> |
1241 | | -<p>1. |
1242 | | -2. |
1243 | | -3. |
1244 | | -4. |
1245 | | -5. |
1246 | | -6.</p> |
| 1240 | +<p>25_CRM_in_chemostat |
| 1241 | +26_CRM_in_serial_dilution |
| 1242 | +41_Structural_stability_in_serial_dilution |
| 1243 | +53_Stochastic_Lotka_Volterra |
| 1244 | +55_Swift_Hohenberg |
| 1245 | +56_temporal_niches</p> |
1247 | 1246 | <h3 id="biochemistry">Biochemistry</h3> |
1248 | | -<p>1.</p> |
| 1247 | +<p>44_two_mer_entropy</p> |
1249 | 1248 | <h3 id="genetics">Genetics</h3> |
1250 | | -<p>1.</p> |
| 1249 | +<p>76_protein_dna_binding</p> |
1251 | 1250 | <h3 id="semiconductor-materials">Semiconductor Materials</h3> |
1252 | | -<p>1. |
1253 | | -2. |
1254 | | -3. |
1255 | | -4. |
1256 | | -5. |
1257 | | -6. |
1258 | | -7.</p> |
| 1251 | +<p>21_Absorption_coefficient_for_alloy_GaAlAs |
| 1252 | +27_Design_trade_offs_for_high_speed_photodetectors |
| 1253 | +34_PN_diode_band_diagram |
| 1254 | +35_Quantum_Dot_Absorption_Spectrum |
| 1255 | +36_Quasi_Fermi_levels_of_photo_resistor_out_of_equilibrium |
| 1256 | +39_Reflection_spectra_for_a_Distributed_Bragg_Reflector |
| 1257 | +42_The_threshold_current_for_multi_quantum_well_lasers</p> |
1259 | 1258 | <h3 id="molecular-modeling">Molecular Modeling</h3> |
1260 | | -<p>1. |
1261 | | -2. |
1262 | | -3. |
1263 | | -4. |
1264 | | -5. |
1265 | | -6.</p> |
1266 | | -<h2 id="example-problem-calculate-chern-numbers-for-the-haldane-model">Example Problem: Calculate Chern numbers for the Haldane Model</h2> |
| 1259 | +<p>47_Internal_Energy |
| 1260 | +51_Simple_Molecular_Dynamics |
| 1261 | +64_GCMC |
| 1262 | +77_Berendsen_thermostat |
| 1263 | +79_Nose_Hoover_chain_thermostat |
| 1264 | +80_Anderson_thermostat</p> |
| 1265 | +<h2 id="example-calculate-chern-numbers-for-the-haldane-model">Example: Calculate Chern numbers for the Haldane Model</h2> |
1267 | 1266 | <h3 id="main-problem-and-dependencies">Main Problem and Dependencies</h3> |
1268 | 1267 | <p><strong>1. Generate an array of Chern numbers for the Haldane model on a hexagonal lattice by sweeping the following parameters: the on-site energy to next-nearest-neighbor coupling constant ratio (<span class="arithmatex">\(m/t_2\)</span> from -6 to 6 with <span class="arithmatex">\(N\)</span> samples) and the phase (<span class="arithmatex">\(\phi\)</span> from -<span class="arithmatex">\(\pi\)</span> to <span class="arithmatex">\(\pi\)</span> with <span class="arithmatex">\(N\)</span> samples) values. Given the lattice spacing <span class="arithmatex">\(a\)</span>, the nearest-neighbor coupling constant <span class="arithmatex">\(t_1\)</span>, the next-nearest-neighbor coupling constant <span class="arithmatex">\(t_2\)</span>, the grid size <span class="arithmatex">\(\delta\)</span> for discretizing the Brillouin zone in the <span class="arithmatex">\(k_x\)</span> and <span class="arithmatex">\(k_y\)</span> directions (assuming the grid sizes are the same in both directions), and the number of sweeping grid points <span class="arithmatex">\(N\)</span> for <span class="arithmatex">\(m/t_2\)</span> and <span class="arithmatex">\(\phi\)</span>.</strong></p> |
1269 | 1268 | <p><div class="highlight"><pre><span></span><code><span class="sd">'''</span> |
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