Question
Answer the following about linear response theory, for 10 points each.
[10m] The change in an operator’s expectation value equals this operation applied to the product of the response function and a perturbation. In classical mechanics, the action equals this operation applied to the Lagrangian.
ANSWER: time integral [or integration with respect to time; accept word forms of integrate in place of “integration” or “integral”; prompt on integral or integration or word forms by asking “with respect to what variable?”]
[10e] The imaginary part of a response function corresponds to this phenomenon. This phenomenon is the release of energy or heat without performing any useful work.
ANSWER: dissipation [or dissipative; accept word forms of dissipate]
[10h] Response functions are calculated from retarded Green’s functions, which are obtained by applying this mathematical procedure to time-ordered Green’s functions. Calculations of the Casimir force either use this procedure or cancel divergences with an appropriate regulator function to obtain the factor of one over 120.
ANSWER: analytic continuation [accept analytic continuation of the Riemann zeta function or analytic continuation of zeta functions; prompt on extending a function’s domain; prompt on continuation]
Data
Team | Opponent | Part 1 | Part 2 | Part 3 | Total |
---|---|---|---|---|---|
Chicago A | Duke A | 10 | 10 | 0 | 20 |
Claremont A | WUSTL B | 10 | 10 | 0 | 20 |
Columbia B | Johns Hopkins A | 10 | 10 | 0 | 20 |
Florida A | Chicago B | 10 | 10 | 0 | 20 |
Georgia Tech A | Brown A | 10 | 10 | 0 | 20 |
Harvard A | Chicago C | 10 | 10 | 0 | 20 |
Illinois A | Georgia Tech B | 10 | 0 | 0 | 10 |
Imperial A | Houston A | 0 | 10 | 0 | 10 |
MIT A | Cornell B | 10 | 10 | 0 | 20 |
Maryland A | Cornell A | 0 | 0 | 0 | 0 |
McGill A | Yale B | 0 | 0 | 0 | 0 |
Michigan A | Minnesota B | 0 | 0 | 0 | 0 |
Minnesota A | UC Berkeley A | 10 | 10 | 0 | 20 |
Northwestern A | Columbia A | 0 | 10 | 0 | 10 |
Ohio State A | Stanford A | 10 | 0 | 0 | 10 |
Penn A | Iowa State A | 10 | 10 | 0 | 20 |
Rutgers A | Penn State A | 10 | 0 | 0 | 10 |
Rutgers B | Purdue A | 10 | 0 | 0 | 10 |
South Carolina A | Virginia A | 0 | 0 | 0 | 0 |
Texas A | Toronto A | 10 | 0 | 0 | 10 |
UC Berkeley B | NYU A | 10 | 10 | 0 | 20 |
Vanderbilt A | Florida B | 0 | 0 | 0 | 0 |
WUSTL A | Yale A | 10 | 10 | 0 | 20 |