(Solved) : Two Level System The Result Of Problerrl4 Is Often Seen In . . .

Two-level system the result of Problerrl4 is often seen in another form. 

(a) If the two energy levels are at Δ and – Δ, show that the energy and heat capacity are U = – Δ tanh (Δ/kBT); C = kB (Δ/kBT)2 sech2 (Δ/kBT). 

(b) If the system has a random composition such that all values of Δ are equally likely up to some limit Δ0, show that the heat capacity is linearly proportional to the temperature, provided kBT << Δ0. This result was applied to the heat capacity of dilute magnetic alloys by W. Marshall, Phys. Rev. 118, 1519 (1960). It is also used in the theory of glasses.

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