Spectra of massive QCD dirac operators from random matrix theory: All three chiral symmetry breaking patterns

The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low-energy correlation functions of all three chiral symmetry breaking patterns (labeled by the Dyson index β = 1, 2 and 4) on the same footing, offering a unifying description of massive QCD Dirac spectra. RMT universality is explicitly proven for all three symmetry classes and the results are compared to the available lattice data for β = 4

A study on the material properties of novel PEGDA/gelatin hybrid hydrogels polymerized by electron beam irradiation

Gelatin-based hydrogels are highly desirable biomaterials for use in wound dressing, drug delivery, and extracellular matrix components due to their biocompatibility and biodegradability. However, insufficient and uncontrollable mechanical properties and degradation are the major obstacles to their application in medical materials. Herein, we present a simple but efficient strategy for a novel hydrogel by incorporating the synthetic hydrogel monomer polyethylene glycol diacrylate (PEGDA, offering high mechanical stability) into a biological hydrogel compound (gelatin) to provide stable mechanical properties and biocompatibility at the resulting hybrid hydrogel. In the present work, PEGDA/gelatin hybrid hydrogels were prepared by electron irradiation as a reagent-free crosslinking technology and without using chemical crosslinkers, which carry the risk of releasing toxic byproducts into the material. The viscoelasticity, swelling behavior, thermal stability, and molecular structure of synthesized hybrid hydrogels of different compound ratios and irradiation doses were investigated. Compared with the pure gelatin hydrogel, 21/9 wt./wt. % PEGDA/gelatin hydrogels at 6 kGy exhibited approximately up to 1078% higher storage modulus than a pure gelatin hydrogel, and furthermore, it turned out that the mechanical stability increased with increasing irradiation dose. The chemical structure of the hybrid hydrogels was analyzed by Fourier-transform infrared (FTIR) spectroscopy, and it was confirmed that both compounds, PEGDA and gelatin, were equally present. Scanning electron microscopy images of the samples showed fracture patterns that confirmed the findings of viscoelasticity increasing with gelatin concentration. Infrared microspectroscopy images showed that gelatin and PEGDA polymer fractions were homogeneously mixed and a uniform hybrid material was obtained after electron beam synthesis. In short, this study demonstrates that both the presence of PEGDA improved the material properties of PEGDA/gelatin hybrid hydrogels and the resulting properties are fine-tuned by varying the irradiation dose and PEGDA/gelatin concentration

Smallest Dirac Eigenvalue Distribution from Random Matrix Theory

We derive the hole probability and the distribution of the smallest eigenvalue of chiral hermitian random matrices corresponding to Dirac operators coupled to massive quarks in QCD. They are expressed in terms of the QCD partition function in the mesoscopic regime. Their universality is explicitly related to that of the microscopic massive Bessel kernel.Comment: 4 pages, 1 figure, REVTeX. Minor typos in subscripts corrected. Version to appear in Phys. Rev.

Microscopic universality of complex matrix model correlation functions at weak non-Hermiticity

The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex matrices, we can prove that all k-point correlation functions including an arbitrary number of Dirac mass terms are universal close to the origin. To this aim we establish the universality of the asymptotics of orthogonal polynomials in the complex plane. The universality of the correlation functions then follows from that of the kernel of orthogonal polynomials and a mapping of massive to massless correlators

Parametric level statistics in random matrix theory: Exact solution

An exact solution to the problem of parametric level statistics in non-Gaussian ensembles of N by N Hermitian random matrices with either soft or strong level confinement is formulated within the framework of the orthogonal polynomial technique. Being applied to random matrices with strong level confinement, the solution obtained leads to emergence of a new connection relation that makes a link between the parametric level statistics and the scalar two-point kernel in the thermodynamic limit.Comment: 4 pages (revtex

New critical matrix models and generalized universality

We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue density vanishes as an arbitrary real power at the origin, thus defining a new class of multicritical matrix models. The corresponding microscopic scaling law is given and possible applications to the chiral phase transition in QCD are discussed. For generic coupling constants off-criticality we prove that all microscopic correlation functions at the origin of the spectrum remain in the known Bessel universality class. An arbitrary number of Dirac mass terms can be included and the corresponding massive universality is maintained as well. We also investigate the critical behavior at the edge of the spectrum: there, in contrast to the behavior at the origin, we find the same critical exponents as derived from matrix models with a polynomial action

Microscopic universality with dynamical fermions

It has recently been demonstrated in quenched lattice simulations that the distribution of the low-lying eigenvalues of the QCD Dirac operator is universal and described by random-matrix theory. We present first evidence that this universality continues to hold in the presence of dynamical quarks. Data from a lattice simulation with gauge group SU(2) and dynamical staggered fermions are compared to the predictions of the chiral symplectic ensemble of random-matrix theory with massive dynamical quarks. Good agreement is found in this exploratory study. We also discuss implications of our results.Comment: 5 pages, 3 figures, minor modifications, to appear in Phys. Rev. D (Rapid Commun.

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 eigenvalues 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

Massive chiral random matrix ensembles at beta = 1 & 4 : Finite-volume QCD partition functions

In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition functions are derived in terms of microscopically rescaled mass variables. In limited cases, correlation functions of Dirac eigenvalues and distributions of the smallest Dirac eigenvalue are given as ratios of these partition functions. When all masses are degenerate, our results reproduce the known expressions for the partition functions of zero-dimensional sigma models.Comment: 6 pages, REVTeX 3.1, no figure; (v2) corrected signatures of c'

Distribution of the k-th smallest Dirac operator eigenvalue

Based on the exact relationship to Random Matrix Theory, we derive the probability distribution of the k-th smallest Dirac operator eigenvalue in the microscopic finite-volume scaling regime of QCD and related gauge theories.Comment: REVTeX 3.1, 6 pages, 1 figure. Corrected factors in eqs. (16a) and (16c) and very minor typos (v2