Comment on "Is There a "Most Perfect Fluid" Consistent with Quantum Field Theory?"

This is a comment on hep-th/0702136Comment: 1 page, comment on hep-th/070213

Turbulent Decay of a Passive Scalar in Batchelor Limit: Exact Results from a Quantum-Mechanical Approach

We show that the decay of a passive scalar $\theta$ advected by a random incompressible flow with zero correlation time in Batchelor limit can be mapped exactly to a certain quantum-mechanical system with a finite number of degrees of freedom. The Schroedinger equation is derived and its solution is analyzed for the case when at the beginning the scalar has Gaussian statistics with correlation function of the form $e^{-|x-y|^2}$. Any equal-time correlation function of the scalar can be expressed via the solution to the Schroedinger equation in a closed algebraic form. We find that the scalar is intermittent during its decay and the average of $|\theta|^\alpha$ (assuming zero mean value of $\theta$) falls as $e^{-\gamma_\alpha Dt}$ at large $t$, where $D$ is a parameter of the flow, $\gamma_\alpha=\alpha(6-\alpha)/4$ for $0<\alpha<3$, and $\gamma_\alpha=9/4$ for $\alpha \geq 3$, independent of $\alpha$.Comment: 7 pages, REVTeX. Minor changes, references updated to match the published versio

Hydrodynamics of relativisic systems with broken continuous symmetries

We show how hydrodynamics of relativistic system with broken continuous symmetry can be constructed using the Poisson bracket technique. We illustrate the method on the example of relativistic superfluids.Comment: 3 pages; talk at DPF2000, Columbus, Ohio, August 9-12, 200

Domain walls of high-density QCD

We show that in very dense quark matter there must exist metastable domain walls where the axial U(1) phase of the color-superconducting condensate changes by 2pi. The decay rate of the domain walls is exponentially suppressed and we compute it semiclassically. We give an estimate of the critical chemical potential above which our analysis is under theoretical control.Comment: 4 pages; Eq. (16) corrected, 2 new references added, published versio