New Developments in Non-Hermitian Random Matrix Models

Correlations of eigenvectors for non-Hermitian random-matrix models

“…For non-hermitian M, as ǫ → 0, the block structure does not decouple, leading to a non-holomorphic resolvent for certain two-dimensional domains on the z-plane. For more technical details we refer to the original work [4], or recent reviews [14,15]. Similar constructions have been proposed recently in [5,16].…”

Hydrodynamical description of the QCD Dirac spectrum at finite chemical potential

“…The random matrix approach has proven to be a useful tool for understanding aspects of chiral symmetry directly from the QCD Dirac spectra both in vacuum and in matter [1,13,14]. The chief idea is the following: for the purpose of analyzing the spontaneous breaking and/or restoration of chiral symmetry, only the low lying eigenmodes of the QCD Dirac operator are important.…”

“…The matrix models at finite µ [9,11] capture this essential aspect of the lattice spectra and the nature of the chiral phase transition [1,13,14]. For a 2-matrix model, the partition function is [11,12] …”

“…1 we display the distribution of eigenvalues following from the 2-matrix model with A and B sampled from a gaussian ensemble of 200×200 matrices with ν = 0 and µ = 0.3. The boundary curves follow from the analysis in [13,16]. The domain is an ellipse x 2 /a 2 + +y 2 /a 2 − = 1 with semi-axes a 2 ± /2l 2 = 1 ± τ /1 ∓ τ as shown in Fig.…”

“…In the 2-matrix model the deformation is still random and only generic for moderate µ with no strict banding at large µ [11,12]. The 1-matrix approach to QCD at finite µ has been discussed by many [1,13,14].…”