The 17/5 spectrum of the Kelvin-wave cascade

Direct numeric simulation of the Biot-Savart equation readily resolves the 17/5 spectrum of the Kelvin-wave cascade from the 11/3 spectrum of the non-local (in the wavenumber space) cascade scenario by L'vov and Nazarenko. This result is a clear-cut visualisation of the unphysical nature of the 11/3 solution, which was established earlier on the grounds of symmetry.Comment: 2 pages, 1 figur

Comment on ``Hausdorff Dimension of Critical Fluctuations in Abelian Gauge Theories"

Hove, Mo, and Sudbo [Phys. Rev. Lett. 85, 2368 (2000)] derived a simple connection, $\eta + D_H = 2$, between the anomalous scaling dimension $\eta$ of the U(1) universality class order parameter and the Hausdorff dimension $D_H$ of critical loops in loop representations of U(1) models. We show that the above relation is wrong and establish a correct relation that contains a new critical exponent.Comment: In 1 revtex page with 1 figur

Rotational response of superconductors: magneto-rotational isomorphism and rotation-induced vortex lattice

The analysis of nonclassical rotational response of superfluids and superconductors was performed by Onsager (in 1949) \cite{Onsager} and London (in 1950) \cite{London} and crucially advanced by Feynman (in 1955) \cite{Feynman}. It was established that, in thermodynamic limit, neutral superfluids rotate by forming---without any threshold---a vortex lattice. In contrast, the rotation of superconductors at angular frequency ${\bf \Omega}$---supported by uniform magnetic field ${\bf B}_L\propto {\bf \Omega}$ due to surface currents---is of the rigid-body type (London Law). Here we show that, neglecting the centrifugal effects, the behavior of a rotating superconductor is identical to that of a superconductor placed in a uniform fictitious external magnetic filed $\tilde{\bf H}=- {\bf B}_L$. In particular, the isomorphism immediately implies the existence of two critical rotational frequencies in type-2 superconductors.Comment: replaced with published versio

Kolmogorov and Kelvin-Wave Cascades of Superfluid Turbulence at T=0: What is in Between?

As long as vorticity quantization remains irrelevant for the long-wave physics, superfluid turbulence supports a regime macroscopically identical to the Kolmogorov cascade of a normal liquid. At high enough wavenumbers, the energy flux in the wavelength space is carried by individual Kelvin-wave cascades on separate vortex lines. We analyze the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, revealing a chain of three distinct intermediate cascades, supported by local-induction motion of the vortex lines, and distinguished by specific reconnection mechanisms. The most prominent qualitative feature predicted is unavoidable production of vortex rings of the size of the order of inter-vortex distance.Comment: 4 RevTex pages, 1 figure. Quantitative analysis of the regime 2 has been revise

Two-Dimensional Weakly Interacting Bose Gas in the Fluctuation Region

We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii--Kosterlitz--Thouless phase transition point. We argue that this crossover is described by universal (for all weakly interacting |psi|^4 models) relations between thermodynamic parameters of the system, including superfluid and quasi-condensate densities. We establish these relations with high-precision Monte Carlo simulations of the classical |psi|^4 model on a lattice, and check their asymptotic forms against analytic expressions derived on the basis of the mean-field theory.Comment: Revtex, 8 pages, 8 figures; submitted to Phys. Rev. A; extended discussion of effective interaction and of a trapped gas; corrected typo in Eq. (32

Comment on "Phase Diagram of a Disordered Boson Hubbard Model in Two Dimensions"

We prove that previous claims of observing a direct superfluid-Mott insulator transition in the disordered J-current model are in error because numerical simulations were done for too small system sizes and the authors ignored the rigorous theorem.Comment: 1 page, Latex, 1 figur