Two level system the result of Problerrl4 is often seen in another form (a) If the two energy levels are at and , show that the energy and heat capacity are U tanh ( k B T) C k B ( k B T) 2 sech 2 ( k B T) (b) If the system has a random composition such that all values of are equally likely up to s...

a The Boltzmann factor gives directly with t KBT e4 UA 4T Ck dUdt kg AkBT sech A ...

Two-level system the result of Problerrl4 is often seen in another form. (a) If the two energy

Question:

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/k_BT); C = k_B (Δ/k_BT)² sech² (Δ/k_BT).

(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 k_BT << 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.