Few-Body Insights Into the Quantum Hall Problem
Few-Body Insights Into the Quantum Hall Problem
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1. Few-body insights into the Qua…
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2. Untitled: Slide 2
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3. From few to many – How can w…
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4. Fermi Systems in Nature
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5. The Fractional Quantum Hall Ef…
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6. Motivations
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7. few-body hyperspherical toolki…
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8. Some successes of the adiabati…
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9. Strategy of Macek's adiabatic …
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10. Joe Macek's (1968 JPB) adiabat…
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11. Untitled: Slide 11
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12. Universality, from nuclear sca…
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13. Here is our Hamiltonian, which…
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14. Table 6
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15. "Critical number for bosonic c…
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16. Effect of renormalization
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17. Back to the quantum Hall probl…
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18. Potential energy of just 1 2D …
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19. Now go to collective N-body co…
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20. Hypersperical coordinate trans…
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21. In hyperspherical coordinates:
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22. Now apply this adiabatic hyper…
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23. Potential energy curves for N …
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24. K=-M=8 3 particles
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25. K=-M=9 3 particles
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26. K=-M=10 3 particles
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27. The Laughlin 1/3 state is one …
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28. Noninteracting states for K=|M…
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29. Now look at some quantitative …
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30. TESTING ADIABATICITY
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31. The composite-fermion view
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32. Semiconductor quantum dots in …
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33. Filling factor, n
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34. Potential energy landscape at …
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35. Noninteracting Quantum fermion…
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36. How does fixed-node Monte Carl…
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37. Minimum quantum Coulomb potent…
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38. Eigenenergies for 4 particles …
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39. K= -M=9 for N=3
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40. Next: an exploration of the ro…
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41. On the role of exceptional deg…
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42. Connection between the high re…
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43. Devil's staircase
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44. Connections between hyperspher…
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45. Energy vs. Magnetic field
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46. Energy spectrum after solving …
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47. "Devil's Staircase"
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48. Fractional Quantum Hall Effect…
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49. Breathing mode signatures of t…
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50. What have we learned
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51. Other directions to understand…
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52. Conclusions
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53. Demo
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