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]

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Data

TeamOpponentPart 1Part 2Part 3Total
Chicago ADuke A1010020
Claremont AWUSTL B1010020
Columbia BJohns Hopkins A1010020
Florida AChicago B1010020
Georgia Tech ABrown A1010020
Harvard AChicago C1010020
Illinois AGeorgia Tech B100010
Imperial AHouston A010010
MIT ACornell B1010020
Maryland ACornell A0000
McGill AYale B0000
Michigan AMinnesota B0000
Minnesota AUC Berkeley A1010020
Northwestern AColumbia A010010
Ohio State AStanford A100010
Penn AIowa State A1010020
Rutgers APenn State A100010
Rutgers BPurdue A100010
South Carolina AVirginia A0000
Texas AToronto A100010
UC Berkeley BNYU A1010020
Vanderbilt AFlorida B0000
WUSTL AYale A1010020