Calculation of the expansion rate of the three-volume measure in high-energy heavy-ion collisions

In ultrarelativistic heavy-ion collisions the local three-volume measure is expanding in the longitudinal and transverse directions. This is similar to the Hubble-expansion of the universe, except that the former is not locally isotropic. As an example the expansion rate is calculated assuming that the energy-momentum tensor in the central region is that of an ideal fluid, undergoing Bjorken flow in longitudinal direction, and with initial conditions as expected for BNL-RHIC energy. While the longitudinal expansion of three-volume is independent of the energy density of the fluid, in case of 3+1 dimensional expansion the form of the hydrodynamical solution (rarefaction wave or deflagration shock) affects the three-volume expansion rate on the hadronization hypersurface. As a consequence the average expansion rate on that surface depends on the transverse size of the system. This may reflect in an impact-parameter dependence of the formation probability of light nuclei and of the freeze-out temperature of the strong interactions in the system.Comment: 10 Pages REVTEX, 4 Figures; Title slightly modified, 2 new figure

Universality and robustness of revivals in the transverse field XY model

We study the structure of the revivals in an integrable quantum many-body system, the transverse field XY spin chain, after a quantum quench. The time evolutions of the Loschmidt echo, the magnetization, and the single-spin entanglement entropy are calculated. We find that the revival times for all of these observables are given by integer multiples of T-rev similar or equal to L/upsilon(max), where L is the linear size of the system and upsilon(max) is the maximal group velocity of quasiparticles. This revival structure is universal in the sense that it does not depend on the initial state and the size of the quench. Applying nonintegrable perturbations to the XY model, we observe that the revivals are robust against such perturbations: they are still visible at time scales much larger than the quasiparticle lifetime. We therefore propose a generic connection between the revival structure and the locality of the dynamics, where the quasiparticle speed upsilon(max) generalizes into the Lieb-Robinson speed upsilon(LR)

Comment on Dirac spectral sum rules for QCD_3

Recently Magnea hep-th/9907096 , hep-th/9912207 [Phys.Rev.D61, 056005 (2000); Phys.Rev.D62, 016005 (2000)] claimed to have computed the first sum rules for Dirac operators in 3D gauge theories from 0D non-linear sigma models. I point out that these computations are incorrect, and that they contradict with the exact results for the spectral densities unambiguously derived from random matrix theory by Nagao and myself.Comment: REVTeX 3.1, 2 pages, no figure. (v2) redundant part removed, conclusion unchange

Ratios of characteristic polynomials in complex matrix models

We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as their Cauchy transforms, generalizing previous expressions for real eigenvalues. We restrict ourselves to ratios of characteristic polynomials over their complex conjugate

Finding the Pion in the Chiral Random Matrix Vacuum

The existence of a Goldstone boson is demonstrated in chiral random matrix theory. After determining the effective coupling and calculating the scalar and pseudoscalar propagators, a random phase approximation summation reveals the massless pion and massive sigma modes expected whenever chiral symmetry is spontaneously broken.Comment: 3 pages, 1 figure, revte