Biomedical subjects

G Akemann

Publications and source records attributed to G Akemann.

3 recordsLinked to original sources

PubMed2002

Microscopic correlation functions for the QCD Dirac operator with chemical potential.

A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with nonvanishing chemical potential. The new correlation functions derived from it are conjectured to predict the local fluctuations of complex Dirac operator eigenvalues at zero virtuality. The parameter measuring the non-Hermiticity of the random matrix is related to the chemical potential. In the phase with broken chiral symmetry all spectral correlations are calculated for finite matrix size N and in the large-N limit at weak and strong non-Hermiticity. The derivation uses the orthogonality of the Laguerre polynomials in the complex plane.

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PubMed2000

Spectra of massive and massless QCD dirac operators: A novel link

We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index beta = 1,2, and 4) leads to emergence of a connection relation between the spectral statistics of massive and massless Dirac operators. This novel link established for beta-fold degenerate massive fermions is used to explicitly derive (and prove the random matrix universality of) statistics of low-lying spectra of QCD Dirac operators in the presence of SU(2) massive fermions in the fundamental representation ( beta = 1) and SU(N(c)>/=2) massive adjoint fermions ( beta = 4). Comparison with available lattice data for SU(2) dynamical staggered fermions reveals a good agreement.

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PubMed1999

Nonuniversality of compact support probability distributions in random matrix theory.

The two-point resolvent is calculated in the large-n limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with that of the canonical Gaussian ensemble by a nonuniversal part that is given explicitly for all monomial potentials V(M)=M(2p). Moreover, we prove that for the generalized fixed and bounded trace ensemble all k-point resolvents agree in the large-n limit, despite their nonuniversality.

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