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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