Biomedical subjects

Gernot Akemann

Publications and source records attributed to Gernot Akemann.

3 recordsLinked to original sources

PubMed2006

Unquenched complex dirac spectra at nonzero chemical potential: two-color QCD lattice data versus matrix model.

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-color lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real and positive for our choice of two staggered flavors. This enables us to use standard Monte Carlo simulations in testing the influence of the chemical potential and quark mass on complex eigenvalues close to the origin. We find excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular, we detect the effect of unquenching when going to very small quark masses.

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PubMed2005

Statistics of real eigenvalues in Ginibre's ensemble of random real matrices.

The integrable structure of Ginibre's orthogonal ensemble of random matrices is looked at through the prism of the probability p(n,k) to find exactly k real eigenvalues in the spectrum of an n x n real asymmetric Gaussian random matrix. The exact solution for the probability function p(n,k) is presented, and its remarkable connection to the theory of symmetric functions is revealed. An extension of the Dyson integration theorem is a key ingredient of the theory presented.

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PubMed2004

QCD dirac operator at nonzero chemical potential: lattice data and matrix model.

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at a nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.

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