Hydrodynamical evolution near the QCD critical end point

Hydrodynamical calculations have been successful in describing global observables in ultrarelativistic heavy ion collisions, which aim to observe the production of the quark-gluon plasma. On the other hand, recently, a lot of evidence that there exists a critical end point (CEP) in the QCD phase diagram has been accumulating. Nevertheless, so far, no equation of state with the CEP has been employed in hydrodynamical calculations. In this paper, we construct the equation of state with the CEP on the basis of the universality hypothesis and show that the CEP acts as an attractor of isentropic trajectories. We also consider the time evolution in the case with the CEP and discuss how the CEP affects the final state observables, such as the correlation length, fluctuation, chemical freezeout, kinetic freezeout, and so on. Finally, we argue that the anomalously low kinetic freezeout temperature at the BNL Relativistic Heavy Ion Collider suggests the possibility of the existence of the CEP.Comment: 13 pages, 12 figures, accepted for publication in Physical Review

Focusing and the Holographic Hypothesis

The ``screen mapping" introduced by Susskind to implement 't Hooft's holographic hypothesis is studied. For a single screen time, there are an infinite number of images of a black hole event horizon, almost all of which have smaller area on the screen than the horizon area. This is consistent with the focusing equation because of the existence of focal points. However, the {\it boundary} of the past (or future) of the screen obeys the area theorem, and so always gives an expanding map to the screen, as required by the holographic hypothesis. These considerations are illustrated with several axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi

Information Geometry of Entanglement Renormalization for free Quantum Fields

We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher information metric. We show how the geometrical description remains invariant despite there is an irreducible gauge freedom in the definition of the tensor network. The results might help to understand how spacetimes may emerge from distributions of quantum states, or more concretely, from the structure of the quantum entanglement concomitant to those distributions.Comment: 18 pages. 1 eps figure. References added. Some comments adde