Abstract:
In QCD with two flavors of massless quarks, the chiral phase transition is plausibly in the same universality class as the classical four component Heisenberg antiferromagnet. Therefore, renormalization group techniques developed in the study of phase transitions can be applied to calculate the critical exponents which characterize the scaling behaviour of universal quantities near the critical point. This approach to the QCD phase transition has implications both for lattice gauge theory and for heavy ion collisions. Future lattice simulations with longer correlation lengths will be able to measure the various exponents and the equation of state for the order parameter as a function of temperature and quark mass which we describe. In a heavy ion collision, the consequence of a long correlation length would be large fluctuations in the number ratio of neutral to charged pions. Unfortunately, we show that this phenomenon will not occur if the plasma stays close to equilibrium as it cools. If the transition is far out of equilibrium and can be modelled as a quench, it is possible that large volumes of the plasma with the pion field correlated will develop, with dramatic phenomenological consequences. }

Abstract:
The Fredkin three-bit gate is universal for computational logic, and is reversible. Classically, it is impossible to do universal computation using reversible two-bit gates only. Here we construct the Fredkin gate using a combination of six two-body reversible (quantum) operators.

Abstract:
We propose that the recently discovered \Theta baryon is a bound state of four quarks and an antiquark, containing two highly correlated ud-pairs. If so, the \Theta baryon has positive parity, and it lies in an near-ideally mixed SU(3)_{f} \mathbf{\bar{10}}_{f} oplus \mathbf{8}_{f}. The Roper resonance and the P_{11}(1710) fit naturally into this classification. We predict an isospin 3/2 multiplet of \Xi's (S=-2) with J^{\Pi}=\half^{+} around 1750 MeV. A search for manifestly exotic \Xi^{+} and \Xi^{--} in this mass range could provide a sharp test of our proposal. We predict that charm and bottom analogues of the \Theta baryon are stable against strong decays.

Abstract:
In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic quantum field theory. These problems are associated with the existence of an infinite number of degrees of freedom per unit volume. Because of these the microscopic entropy can, and typically does, diverge for sharply localized states. However the difference in the entropy between two such states is better behaved, and for most purposes it is the useful quantity to consider. In particular, a renormalized entropy can be defined as the entropy relative to the ground state. We make these remarks quantitative and precise in a simple model situation: the states of a conformal quantum field theory excited by a moving mirror. From this work, we attempt to draw some lessons concerning the ``information problem'' in black hole physics

Abstract:
It is argued that the qualitative features of black holes, regarded as quantum mechanical objects, depend both on the parameters of the hole and on the microscopic theory in which it is embedded. A thermal description is inadequate for extremal holes. In particular, extreme holes of the charged dilaton family can have zero entropy but non-zero, and even (for $a>1$) formally infinite, temperature. The existence of a tendency to radiate at the extreme, which threatens to overthrow any attempt to identify the entropy as available internal states and also to expose a naked singularity, is at first sight quite disturbing. However by analyzing the perturbations around the extreme holes we show that these holes are protected by mass gaps, or alternatively potential barriers, which remove them from thermal contact with the external world. We suggest that the behavior of these extreme dilaton black holes, which from the point of view of traditional black hole theory seems quite bizarre, can reasonably be interpreted as the holes doing their best to behave like normal elementary particles. The $a<1$ holes behave qualitatively as extended objects.

Abstract:
We propose a symmetry breaking scheme for QCD with three massless quarks at high baryon density wherein the color and flavor SU(3)_color times SU(3)_L times SU(3)_R symmetries are broken down to the diagonal subgroup SU(3)_{color+L+R} by the formation of a condensate of quark Cooper pairs. We discuss general properties that follow from this hypothesis, including the existence of gaps for quark and gluon excitations, the existence of Nambu-Goldstone bosons which are excitations of the diquark condensate, and the existence of a modified electromagnetic gauge interaction which is unbroken and which assigns integral charge to the elementary excitations. We present mean-field results for a Hamiltonian in which the interaction between quarks is modelled by that induced by single-gluon exchange. We find gaps of order 10-100 MeV for plausible values of the coupling. We discuss the effects of nonzero temperature, nonzero quark masses and instanton-induced interactions on our results.

Abstract:
Standard lattice fermion algorithms run into the well-known sign problem at real chemical potential. In this paper we investigate the possibility of using imaginary chemical potential, and argue that it has advantages over other methods, particularly for probing the physics at finite temperature as well as density. As a feasibility study, we present numerical results for the partition function of the two-dimensional Hubbard model with imaginary chemical potential. We also note that systems with a net imbalance of isospin may be simulated using a real chemical potential that couples to I_3 without suffering from the sign problem.

Abstract:
The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices' statistical properties, the statistics of the velocity increments is derived. In particular, the origin and nature of small-scale intermittency in this model is investigated both numerically and analytically.

Abstract:
We use a variational procedure to study finite density QCD in an approximation in which the interaction between quarks is modelled by that induced by instantons. We find that uniform states with conventional chiral symmetry breaking have negative pressure with respect to empty space at all but the lowest densities, and are therefore unstable. This is a precisely defined phenomenon which motivates the basic picture of hadrons assumed in the MIT bag model, with nucleons as droplets of chiral symmetry restored phase. At all densities high enough that the chirally symmetric phase fills space, we find that color symmetry is broken by the formation of a condensate of quark Cooper pairs. A plausible ordering scheme leads to a substantial gap in a Lorentz scalar channel involving quarks of two colors, and a much smaller gap in an axial vector channel involving quarks of the third color.

Abstract:
We demonstrate when p-wave pairing occurs between species whose free Fermi surfaces are mismatched the gap generally vanishes over a two-dimensional surface. We present detailed calculations of condensation energy, superfluid density (Meissner mass) and specific heat for such states. We also consider stability against separation into mixed phases. According to several independent criteria that can be checked at weak coupling, the resulting ``breached'' state appears to be stable over a substantial range of parameters. The simple models we consider are homogeneous in position space, and break rotation symmetry spontaneously. They should be realizable in cold atom systems.