Exam distribution

Rubrics used for the grading

Part 1a (34 points) : Cv or chi (fluctuation dissipation)
        100 %: practically perfect
         75 %: dimension not correct, otherwise correct
         25 %: correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 1b (34 points) : equipartition theorem: semi-classical, k_B T/2 per quadratic degree of freedom
        100 %: practically perfect
         80 %: did not mention "(semi-)classical" or "quadratic degree of freedom" but correct otherwise, and gave some valid examples
         80 %: did not mention "quadratic" degree of freedom but correct otherwise
         60 %: did not mention "(semi-)classical" or "quadratic degree of freedom" but correct otherwise
         25 %: correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 1c (34 points) : Equipartition theorem -- still useful in the quantum regime
        100 %: practically perfect
         75 %: correct answer, insufficient reason (did not realize that it is useful even in the quantum degenerate regime)
         60 %: incorrect answer, but all reasons to give the correct answer are listed
         40 %: incorrect answer, but point of view explained well
         25 %: incorrect answer, with valid but irrelevant discussion
         25 %: correct answer deduced from incorrect reasons!
          0 %: answer missing, or completely incorrect
Part 1d (34 points) : 
         40 %: outline provided, but insufficient calculation to support the answer
         33 %: correct answer, but derived simply from E, which is not explained.
          0 %: answer missing, or completely incorrect
Part 2a1 (25 points) : exp(beta mu) = n lambda^3, for the volume gas
        100 %: practically perfect
         60 %: correct starting formula, mistakes lead to incorrect result at end
         25 %: correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 2a2 (25 points) : exp(beta (mu + phi)) = n_A lambda^2, for the surface gas
        100 %: practically perfect
         80 %: correct except the incorrect power of lambda
         50 %: correct starting point, derived an answer, incorrect due to mistake
         25 %: incorrect due to incorrect assumptions
         25 %: correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 2a3 (25 points) : equate mu and T (between surface and volume gases) to get n_A = P beta lambda exp(beta phi)
         95 %: would have been perfect, were it not for (numerical) mistakes accumulated from previous part(s)
         33 %: almost correct answer (lambda missing) but due to considering the surface gas only and mis-attributing P of surface to P of bulk
         25 %: stated, incorrectly, G_s = G_v, and no result from it
          0 %: answer missing, or completely incorrect
Part 2b (25 points) : n_A = 0 when the volume gas is in the BEC phase
         25 %: correct starting formula, but no or little development from it
         25 %: correct answer deduced from incorrect reasons!
          0 %: answer missing, or completely incorrect
Part 3a1 (23 points) : mean field model: H_i -- eigenvalues
        100 %: practically perfect
         50 %: H_i set, but eigenvalues were not considered
         33 %: H_i was misidentified (sigma_x term or sigma_z term not inluded)
          0 %: answer missing, or completely incorrect
Part 3a2 (22 points) : Z from H_i eigenvalues
        100 %: practically perfect
         95 %: would have been perfect, were it not for (numerical) mistakes accumulated from previous part(s)
         25 %: correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 3a3 (23 points) : m_z, m_x from Z, by differentiation
         95 %: would have been perfect, were it not for (numerical) mistakes accumulated from previous part(s)
         90 %: correct except that a sign is incorrect
         80 %: logically correct answer from previous incorrect part(s), but with some error (e.g. sign mistake)
         50 %: one of m_z, m_x, would have been perfect, were it not for mistakes accumulated from previous part(s)
          0 %: answer missing, or completely incorrect
Part 3b (22 points) : h = 0: m_z = tanh (beta J z m_z) like in class, and T_c = J z / k_B
        100 %: practically perfect
         95 %: would have been perfect, were it not for (numerical) mistakes accumulated from previous part(s)
         60 %: m_z equation set correctly (or logically correctly from a previously incorrect answer), but T_c incorrectly deduced
         25 %: correct answer stated with no derivation
          0 %: answer missing, or completely incorrect
Part 3c (10 points) : chi_x = mu_B beta,  chi_z = 0
         95 %: would have been perfect, were it not for (numerical) mistakes accumulated from previous part(s)
         50 %: while logically correct from previous incorrect part(s), answers are far from physical
         25 %: correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 4a1 (25 points) : Z for the system set up correctly (including the lid)
        100 %: practically perfect
         75 %: correct except that p_y was not considered
         50 %: did not do the lid, but only gas (and included gravity for the gas, despite the instruction not to)
         25 %: correct starting formula, but no or little development from it
Part 4a2 (25 points) : Z integrated correctly?
         75 %: expressed as a y-sum, which was not evaluated/integrated.
         60 %: y was not integrated over
         60 %: integrated the gas part, without/despite noticing that it depends on y
         60 %: did not include the volume integral for the gas part
         25 %: correct starting formula, but no or little development from it
Part 4b1 (25 points) : -k_B T log Z_{gas} = Gibbs free energy in this case, per principle
        100 %: practically perfect
         25 %: correct answer deduced from incorrect reasons!
          0 %: answer missing, or completely incorrect
Part 4b2 (25 points) : -k_B T log Z_{gas} = Gibbs free energy in this case, per calculation
        100 %: practically perfect
         95 %: would have been perfect, were it not for (numerical) mistakes accumulated from previous part(s)
         75 %: discussion is valid, but did not really connect to part a
         50 %: tried proving it, in a logically consistent manner from the previous part, but without success
         25 %: only general case discussed, not this case, which required examination
          0 %: answer missing, or completely incorrect