The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-

Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method can be applied to any system with a complex action, and it eliminates the so-called overlap problem completely. We test the new approach in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density. The achieved system size is large enough to extract the thermodynamic limit. Our results provide a clear understanding of how the expected first order phase transition is induced by the imaginary part of the action.Comment: 27 pages, 25 figure

Chiral symmetry restoration and the Z3 sectors of QCD

Quenched SU(3) lattice gauge theory shows three phase transitions, namely the chiral, the deconfinement and the Z3 phase transition. Knowing whether or not the chiral and the deconfinement phase transition occur at the same temperature for all Z3 sectors could be crucial to understand the underlying microscopic dynamics. We use the existence of a gap in the Dirac spectrum as an order parameter for the restoration of chiral symmetry. We find that the spectral gap opens up at the same critical temperature in all Z3 sectors in contrast to earlier claims in the literature.Comment: 4 pages, 4 figure

Variance of transmitted power in multichannel dissipative ergodic structures invariant under time reversal

We use random matrix theory (RMT) to study the first two moments of the wave power transmitted in time reversal invariant systems having ergodic motion. Dissipation is modeled by a number of loss channels of variable coupling strength. To make a connection with ultrasonic experiments on ergodic elastodynamic billiards, the channels injecting and collecting the waves are assumed to be negligibly coupled to the medium, and to contribute essentially no dissipation. Within the RMT model we calculate the quantities of interest exactly, employing the supersymmetry technique. This approach is found to be more accurate than another method based on simplifying naive assumptions for the statistics of the eigenfrequencies and the eigenfunctions. The results of the supersymmetric method are confirmed by Monte Carlo numerical simulation and are used to reveal a possible source of the disagreement between the predictions of the naive theory and ultrasonic measurements.Comment: 10 pages, 2 figure

Statistics of Atmospheric Correlations

For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show that the random matrix approach can be beneficially applied to a completely different classical domain, namely, to the empirical correlation matrices obtained from the analysis of the basic atmospheric parameters that characterise the state of atmosphere. We show that the spectrum of atmospheric correlation matrices satisfy the random matrix prescription. In particular, the eigenmodes of the atmospheric empirical correlation matrices that have physical significance are marked by deviations from the eigenvector distribution.Comment: 8 pages, 9 figs, revtex; To appear in Phys. Rev.

Chaos Driven Decay of Nuclear Giant Resonances: Route to Quantum Self-Organization

The influence of background states with increasing level of complexity on the strength distribution of the isoscalar and isovector giant quadrupole resonance in $^{40}$Ca is studied. It is found that the background characteristics, typical for chaotic systems, strongly affects the fluctuation properties of the strength distribution. In particular, the small components of the wave function obey a scaling law analogous to self-organized systems at the critical state. This appears to be consistent with the Porter-Thomas distribution of the transition strength.Comment: 14 pages, 4 Figures, Illinois preprint P-93-12-106, Figures available from the author

Second and Third Order Observables of the Two-Matrix Model

In this paper we complement our recent result on the explicit formula for the planar limit of the free energy of the two-matrix model by computing the second and third order observables of the model in terms of canonical structures of the underlying genus g spectral curve. In particular we provide explicit formulas for any three-loop correlator of the model. Some explicit examples are worked out.Comment: 22 pages, v2 with added references and minor correction

Discretization Effects in the ϵ Domain of QCD

Kieburg M, Verbaarschot JJM, Zafeiropoulos S. Discretization Effects in the ϵ Domain of QCD. In: Proceedings, 31st International Symposium on Lattice Field Theory (Lattice 2013). PoS Lattice2013. 2014: 120.At nonzero lattice spacing the QCD partition function with Wilson quarks undergoes either a second order phase transition to the Aoki phase for decreasing quark mass or shows a first order jump when the quark mass changes sign. We discuss these phase transitions in terms of Wilson Dirac spectra and show that the first order scenario can only occur in the presence of dynamical quarks while in the quenched case we can only have a transition to the Aoki phase. The exact microscopic spectral density of the non-Hermitian Wilson Dirac operator with dynamical quarks is discussed as well. We conclude with some remarks on discretization effects for the overlap Dirac operator

Random matrix approach to three-dimensional QCD with a Chern-Simons term

Kanazawa T, Kieburg M, Verbaarschot JJM. Random matrix approach to three-dimensional QCD with a Chern-Simons term. arXiv:1904.03274. 2019.We propose a random matrix theory for QCD in three dimensions with a Chern-Simons term at level $k$ which spontaneously breaks the flavor symmetry according to U($2N_{\rm f}$) $\to$ U($N_{\rm f}+k$)$\times$U($N_{\rm f}-k$). This random matrix model is obtained by adding a complex part to the action for the $k=0$ random matrix model. We derive the pattern of spontaneous symmetry breaking from the analytical solution of the model. Additionally, we obtain explicit analytical results for the spectral density and the spectral correlation functions for the Dirac operator at finite matrix dimension, that become complex. In the microscopic domain where the matrix size tends to infinity, they are expected to be universal, and give an exact analytical prediction to the spectral properties of the Dirac operator in the presence of a Chern-Simons term. Here, we calculate the microscopic spectral density. It shows exponentially large (complex) oscillations which cancel the phase of the $k=0$ theory

Discretization effects in the ε domain of QCD

At nonzero lattice spacing the QCD partition function with Wilson quarks undergoes either a second order phase transition to the Aoki phase for decreasing quark mass or shows a first order jump when the quark mass changes sign. We discuss these phase transitions in terms of Wilson Dirac spectra and show that the first order scenario can only occur in the presence of dynamical quarks while in the quenched case we can only have a transition to the Aoki phase. The exact microscopic spectral density of the non-Hermitian Wilson Dirac operator with dynamical quarks is discussed as well. We conclude with some remarks on discretization effects for the overlap Dirac operator

Isolation of polymorphic microsatellite loci from the flea beetle Phyllotreta nemorum L. (Coleoptera: Chrysomelidae)

Ten microsatellite markers for the flea beetle Phyllotreta nemorum were developed using di- and trinucleotide repeat-enriched libraries. Each of these primer pairs were characterized on 96 individuals. Expected heterozygosities ranged between 0.11 and 0.84 and the number of alleles ranged between two and 14 per locus. These microsatellite markers are the first published for any Phyllotreta specie