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
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.