AG Mathematische Physik, Martin Ravn (München): Spectral Estimates for Fermionic n-Body Operators - Old and New

Martin Ravn (München)

Spectral Estimates for Fermionic n-Body Operators – Old and New

Abstract:

We consider bounds on the eigenvalues of the n-body operators associated
to fermionic N-particle states. We review the classic norm estimates of
Yang, and present a recent estimate on the Hilbert-Schmidt norm of
2-body operators and their truncated versions.

The Hilbert-Schmidt estimate is interesting since it is of the same
order as the optimal norm estimate, O(N). This implies that although a
fermionic 2-body operator can have eigenvalues of size ~N, it can not
have too many large eigenvalues.