I am a student doing physics hons and have had very little experience in programming. This semester we are supposed to do a computational project in thermodynamics. I have to solve these two coupled diff eqns:
$$ \begin{aligned} ω (p,T ) &= \frac{p ^2}{2m} + \frac{2}{N}\sum_q f(p − q)\,n (q) − \frac{1}{N^2}\sum_{s,t} f(s − t)\,n(s)\,n(t) \quad\text{and} \\ n(p) &= \frac{1}{\exp\left[\cfrac{ω (p,T ) − \mu}{kT}\right] − 1} \end{aligned} $$
$\omega$ is the energy per boson.
$p$ is the momentum of a boson.
$n(p)$ is the number of bosons in the state with momentum $p$.
$f$ is a function of the form $$ f(p)=\frac{1}{2} \left[\epsilon_0- \frac{p^2}{2m}\right] $$
$\epsilon_0$ is elementary excitation energy at 0 K.
$N$ is total no of bosons.
$T$ is temp and $k$ is a constant.
Can someone guide me to any simple methods to generate some crude solution to this problem? Based on a paper: "Evaluation of specific heat for superfluid helium between 0 - 2.1 K based on nonlinear theory" By Shosuke Sasaki (arXiv:0807.1361v1 [cond-mat.other] 9 Jul 2008
