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Abstract: Usually, we study the statistical behaviours of noninteracting Fermions infinite mainly two and three dimensions. For a fixed number of fermions, theaverage energy per fermion is calculated in two and in three dimensions and itbecomes equal to 50 and 60 per cent of the fermi energy respectively. However,in the higher dimensions this percentage increases as the dimensionalityincreases and in infinite dimensions it becomes 100 per cent. This is anintersting result, at least pedagogically. Which implies all fermions aremoving with Fermi momentum. This result is not yet discussed in standard textbooks of quantum statistics. In this paper, this fact is discussed andexplained. I hope, this article will be helpful for graduate students to studythe behaviours of free fermions in generalised dimensionality.



Autor: Muktish Acharyya Department of Physics, Presidency College, Calcutta, India

Fuente: https://arxiv.org/



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