September 2011
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## On the Eigenvalue Density of the non-Hermitian Wilson Dirac Operator

Mario Kieburg, Jacobus J.M. Verbaarschot, Savvas Zafeiropoulos

We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the $$\epsilon$$-domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition to the density of the complex eigenvalues we also obtain the density of the real eigenvalues separately for positive and negative chiralities as well as an explicit analytical expression for the number of additional real modes.

http://arxiv.org/abs/1109.0656
High Energy Physics – Lattice (hep-lat); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)

## Non linear pseudo-bosons versus hidden Hermiticity

Fabio Bagarello, Miloslav Znojil

The increasingly popular concept of a hidden Hermiticity of operators (i.e., of their Hermiticity with respect to an {\it ad hoc} inner product in Hilbert space) is compared with the recently introduced notion of {\em non-linear pseudo-bosons}. The formal equivalence between these two notions is deduced under very general assumptions. Examples of their applicability in quantum mechanics are discussed.

http://arxiv.org/abs/1109.0605
Mathematical Physics (math-ph); Functional Analysis (math.FA); Quantum Physics (quant-ph)