Question
Name some useful ways to rewrite the fermionic creation and annihilation operators, a and a-dagger, when doing condensed matter physics, for 10 points each.
[10m] In some 1D topological materials, rewriting a and a-dagger in terms of operators named for this physicist yields namesake “zero modes” that may be used as stable qubits. Particles that are their own antiparticles are named for this physicist.
ANSWER: Ettore Majorana (“ma-yo-RA-na”) [accept Majorana operators or Majorana zero modes]
[10e] When treating crystals, a and a-dagger can be expressed in the momentum basis by applying this operation. This operation named for a French mathematician outputs a function’s component frequencies.
ANSWER: Fourier transform [or FT]
[10h] Hamiltonians that are quadratic in a and a-dagger, such as those of superconductors and superfluids, can be diagonalized with this transformation. For fermions, this transformation’s coefficients u and v are parametrized as sine theta and cosine theta.
ANSWER: Bogoliubov transformation
<Physics>
Summary
| 2024 ACF Regionals @ Berkeley | 01/27/2024 | Y | 3 | 13.33 | 100% | 33% | 0% |
| 2024 ACF Regionals @ Cornell | 01/27/2024 | Y | 3 | 6.67 | 67% | 0% | 0% |
| 2024 ACF Regionals @ JMU | 01/27/2024 | Y | 6 | 13.33 | 67% | 50% | 17% |
| 2024 ACF Regionals @ Minnesota | 01/27/2024 | Y | 2 | 15.00 | 50% | 50% | 50% |
| 2024 ACF Regionals @ Nebraska | 01/27/2024 | Y | 5 | 8.00 | 80% | 0% | 0% |
| 2024 ACF Regionals @ Rutgers | 01/27/2024 | Y | 4 | 17.50 | 100% | 75% | 0% |
| 2024 ACF Regionals @ Imperial | 01/27/2024 | Y | 4 | 17.50 | 100% | 50% | 25% |
Data
| Cambridge B | Cambridge C | 0 | 10 | 0 | 10 |
| Imperial B | KCL | 10 | 10 | 0 | 20 |
| Kiel | Oxford B | 0 | 10 | 0 | 10 |
| Oxford A | Edinburgh | 10 | 10 | 10 | 30 |