I'm applying to PhD programs in physics. However, there are no good research opportunities at my school. I have produced no original results that I can talk about so far, and I'm worried that I will be competing with candidates who have several publications, original results, and so onforth. However, I independently studied some subjects in depth, for. For instance, some topics in condensed matter theory topics, such as topological order, the quantum hall effect, the renormalization group technique which, I think, are normally studied at graduate not undergraduate level. Is it appropriate to elaborate in my statement of purpose at length about the topics that I have studied and the calculations that I have done even if these are not original results of mine? Otherwise, I will not have much to say about my academic experience.