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There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.

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We report on the evidence from photoluminescence measurements of the relative positions of the localized d-levels of the Mn2+ ions with respect to the conduction and valence bands of Cd1−xMnxTe. The results indicate that the ground state 6S is approximately 0.8 eV inside the valence band for all compositions up to x=0.7. The first excited state 4G is deep inside the gap, and it represents an energy level that may substantially affect the lifetime and recombination characteristics of the carriers in the Cd1−xMnxTe system.