Related papers: Multicritical Matrix Models and the Chiral Phase T…
Universality in unitary invariant random matrix ensembles with complex matrix elements is considered. We treat two general ensembles which have a determinant factor in the weight. These ensembles are relevant, e.g., for spectra of the Dirac…
We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few body operators in chaotic many-body…
It is believed at present that the chiral transition changes from a smooth crossover to a first-order transition at low temperatures and high densities. Such regime is commonly analyzed using effective models since first principle…
We investigate the eigenvalue spectrum of the staggered Dirac matrix in full QCD with two colors and finite chemical potential. Along the strong-coupling axis up to the temperature phase transition, the low-lying Dirac spectrum is well…
Large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions are calculated for SU(2) lattice gauge theory. The accumulation of eigenvalues near zero is analyzed as a signal of chiral symmetry breaking and…
Finite-volume modifications of the two-flavor chiral phase diagram are investigated within an effective quark-meson model in various mean-field approximations. The role of vacuum fluctuations and boundary conditions, their influence on…
The low temperature behaviour of the four-state chiral clock ($CC_4$) model is reexamined using a systematic low temperature series expansion of the free energy. Previously obtained results for the low temperature phases are corrected and…
We investigate finite-size effects on the chiral phase diagram of strong interactions within the linear sigma model coupled to quarks. We estimate the modification of the pseudocritical transition line and isentropic trajectories for sizes…
The microscopic spectrum of the QCD Dirac operator is shown to obey random matrix model statistics in the bulk region of the spectrum close to the origin using finite-volume partition functions.
In these lectures we review recent results on universal fluctuations of QCD Dirac spectra and applications of Random Matrix Theory (RMT) to QCD. We review general properties of Dirac spectra and discuss the relation between chiral symmetry…
Density fluctuations of intranuclear matter suffering collisions with projectile particles are capable to turn into multiquark clusters with chiral symmetry restored. Theoretical analysis of these processes requires an additional taking…
Low lying scalar resonances emerge as a necessary part to adjust chiral perturbation theory to experimental data once unitarity constraint is taken into consideration. I review recent progress made in this direction in a model independent…
We consider angular dependence of the diffractive dissociation processes at high energies. It appeared that angular dependence of the diffractive dissociation has no dip and bump structure at the LHC energies and would show a smooth…
It is shown that the simplest multiplicative random complex matrix model generalizes the large-N phase structure found in the unitary case: A perturbative regime is joined to a nonperturbative regime at a point of nonanalyticity.
We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both…
Universality, where microscopic details become irrelevant, takes place in thermodynamic phase transitions. The universality is captured by a singular scaling function of the thermodynamic variables, where the scaling exponents are…
Rapid rotation may exist in physical systems such as non-central heavy ion collisions and neutron stars. Using functional renormalization group analysis of the quark-meson model, we investigate the effects of real and imaginary rotation on…
For one flavour, we observe that standard chiral random matrix models are schematic variants of the Nambu-Jona-Lasinio (NJL) models whether in vacuum or matter. The ensuing thermodynamics is that of constituent quarks, with mean-field…
We show that, with an appropriate choice of a Dirac operator, there is a remnant of chiral anomalies in the reduced model in which there is no coordinate dependences of the gauge field. This result is obtained by exploring a topological…
If QCD is to undergo a second order phase transition, the light quark return probability is universal for large times at the critical point. We show that this behavior is distinct from the one expected at the mobility edge of a…