Speaker
Description
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size, and which very quickly become too large to be addressed by the computer. A related problem is that the computational time for the most obvious brute-force method scales exponentially with the system size which makes it difficult to study the system in the large N limit. Our methods address these issues in a systematic and hierarchical manner. We apply our methods to a simple model with single particle energy spectrum given by ε(p, q) = ε0 (p2 + q 4 ), where p and q are non-negative integers. However, our methods are very general and applicable to a wide class of problems. Working within the microcanonical ensemble, our methods enable one to directly monitor the approach to the thermodynamic limit (N → ∞), and in so doing, the equivalence with the canonical ensemble is made more manifest. Various thermodynamic quantities as a function of N may be computed using our methods; in this paper, we focus on the entropy, the chemical potential and the temperature.
| Would you like to <br> submit a short paper <br> for the Conference <br> Proceedings (Yes / No)? | no |
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| Level (Hons, MSc, <br> PhD, other)? | other |
| Consider for a student <br> award (Yes / No)? | no |
