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The Sign Problem is the Solution
J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot
The unquenched spectral density of the Dirac operator at is complex and has oscillations with a period inversely proportional to the volume and an amplitude that grows exp…
Random Matrices
M. A. Stephanov, J. J. M. Verbaarschot, T. Wettig
We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide…
Chiral Symmetry Breaking at Nonzero Chemical Potential
J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot
We consider chiral symmetry breaking at nonzero chemical potential and discuss the relation with the spectrum of the Dirac operator. We solve the so called Silver Blaze Problem tha…
Sum Rules for the Dirac Spectrum of the Schwinger Model
L. Shifrin, J. J. M. Verbaarschot
The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In this paper we give a micr…
QCD, Chiral Random Matrix Theory and Integrability
J. J. M. Verbaarschot
Random Matrix Theory has been a unifying approach in physics and mathematics.In these lectures we discuss applications of Random Matrix Theory to QCD and emphasize underlying integ…