Question
When in a collinear configuration, the spectrum of this quantum system can be computed with impressive accuracy by quantizing its unstable classical orbits using the Gutzwiller trace formula. For 10 points each:
[10m] Name this system, whose potential energy in atomic units is “negative 2 over r1 minus 2 over r2 plus 1 over r1 minus r2.” The final repulsive term prevents this system from being exactly solvable, unlike a lighter counterpart.
ANSWER: helium atom [reject “helium nucleus” or “alpha particle”]
[10e] The helium atom is important in quantum chaos because the dynamics of its two electrons and nucleus are similar to this chaotic classical system, which is exemplified by the Moon, Sun, and Earth.
ANSWER: three-body problem [prompt on n-body problem]
[10h] For a generic chaotic Hamiltonian, the gaps in the spectrum are distributed according to this physicist’s namesake “surmise.” The phase space formulation of QM is based on this physicist’s “quasiprobability” distribution.
ANSWER: Eugene Wigner
<VD, Physics>
Summary
| 2023 ARCADIA at UC Berkeley | Premiere | Y | 2 | 25.00 | 100% | 100% | 50% |
| 2023 ARCADIA at Carleton University | Premiere | Y | 3 | 13.33 | 67% | 67% | 0% |
| 2023 ARCADIA at Claremont Colleges | Premiere | Y | 1 | 20.00 | 100% | 100% | 0% |
| 2023 ARCADIA at Indiana | Premiere | Y | 5 | 8.00 | 60% | 20% | 0% |
| 2023 ARCADIA at RIT | Premiere | Y | 2 | 25.00 | 100% | 100% | 50% |
| 2023 ARCADIA at WUSTL | Premiere | Y | 3 | 6.67 | 67% | 0% | 0% |
| 2023 ARCADIA at Duke | Emory, Duke, Yale | N | 4 | 7.50 | 75% | 0% | 0% |
| 2023 ARCADIA at Emory | Emory, Duke, Yale | N | 4 | 10.00 | 75% | 25% | 0% |
| 2023 ARCADIA at Imperial | Imperial | N | 5 | 16.00 | 80% | 60% | 20% |
| 2023 ARCADIA at Maryland | Maryland, Online | N | 3 | 16.67 | 100% | 67% | 0% |
| 2023 ARCADIA at Ohio State | Ohio State, Texas | N | 3 | 13.33 | 100% | 33% | 0% |
| 2023 ARCADIA Online | Maryland, Online | N | 3 | 20.00 | 100% | 67% | 33% |
| 2023 ARCADIA at Texas | Ohio State, Texas | N | 3 | 13.33 | 67% | 67% | 0% |
Data
| Berkeley A | Berkeley C | 10 | 10 | 10 | 30 |
| Berkeley B | Stanford A | 10 | 10 | 0 | 20 |
| Ottawa A | McDouble West-Carleton | 0 | 10 | 0 | 10 |
| Toronto Ray of Sun in the Sky | Ottawa C | 10 | 10 | 0 | 20 |
| Ottawa B | Waterloo | 10 | 0 | 0 | 10 |
| SGV Capital | I will play anything with a buzzer in front of me | 10 | 10 | 0 | 20 |
| Purdue A | Chicago B | 0 | 10 | 0 | 10 |
| Illinois B | Notre Dame A | 0 | 0 | 0 | 0 |
| Illinois A | Notre Dame B | 10 | 10 | 0 | 20 |
| Chicago A | Purdue B | 0 | 10 | 0 | 10 |
| Vanderbilt | Indiana | 0 | 0 | 0 | 0 |
| RIT | Cornell MATLAB | 10 | 10 | 10 | 30 |
| Cornell R | Syracuse+Rochester | 10 | 10 | 0 | 20 |
| Missouri A | Squidward Community College | 0 | 10 | 0 | 10 |
| SIUE | WUSTL H2O | 0 | 0 | 0 | 0 |
| WUSTL XYZ | Missouri B | 0 | 10 | 0 | 10 |