629 research outputs found
Comment on "Symmetries and Interaction Coefficients of Kelvin waves" [arXiv:1005.4575] by Lebedev and L'vov
We comment on the claim by Lebedev and L'vov [arXiv:1005.4575] that the
symmetry with respect to a tilt of a quantized vortex line does not yet
prohibit coupling between Kelvin waves and the large-scale slope of the line.
Ironically, the counterexample of an effective scattering vertex in the local
induction approximation (LIA) attempted by Lebedev and L'vov invalidates their
logic all by itself being a notoriously known example of how symmetries impose
stringent constraints on kelvon kinetics---not only the coupling in question
but the kinetics in general are absent within LIA. We further explain that the
mistake arises from confusing symmetry properties of a specific mathematical
representation in terms of the canonical vortex position field w(z) = x(z) +
iy(z), which explicitly breaks the tilt symmetry due to an arbitrary choice of
the z-axis, with those of the real physical system recovered in final
expressions.Comment: comment on arXiv:1005.4575, version accepted in JLTP with minimal
changes: abstract adde
On role of symmetries in Kelvin wave turbulence
E.V. Kozik and B.V. Svistunov (KS) paper "Symmetries and Interaction
Coefficients of Kelvin waves", arXiv:1006.1789v1, [cond-mat.other] 9 Jun 2010,
contains a comment on paper "Symmetries and Interaction coefficients of Kelvin
waves", V. V. Lebedev and V. S. L'vov, arXiv:1005.4575, 25 May 2010. It relies
mainly on the KS text "Geometric Symmetries in Superfluid Vortex Dynamics}",
arXiv:1006.0506v1 [cond-mat.other] 2 Jun 2010. The main claim of KS is that a
symmetry argument prevents linear in wavenumber infrared asymptotics of the
interaction vertex and thereby implies locality of the Kelvin wave spectrum
previously obtained by these authors. In the present note we reply to their
arguments. We conclude that there is neither proof of locality nor any
refutation of the possibility of linear asymptotic behavior of interaction
vertices in the texts of KS
Symmetries and Interaction coefficients of Kelvin waves
We considered symmetry restriction on the interaction coefficients of Kelvin
waves and demonstrated that linear in small wave vector asymptotic is not
forbidden, as one can expect by naive reasoning.Comment: 4 pages, submitted to J. of Low Temp. Phy
Comment on "Symmetries and Interaction Coefficients of Kelvin wavesâ byLebedev andL'vov
We comment on the claim by Lebedev and L'vov (J. Low Temp. Phys. 161, 2010) that the symmetry with respect to a tilt of a quantized vortex line does not yet prohibit coupling between Kelvin waves and the large-scale slope of the line. Ironically, the counterexample of an effective scattering vertex in the local induction approximation (LIA) attempted by Lebedev and L'vov invalidates their logic all by itself being a notoriously known example of how symmetries impose stringent constraints on kelvon kineticsânot only the coupling in question but the kinetics in general are absent within LIA. We further explain that the mistake arises from confusing symmetry properties of a specific mathematical representation in terms of the canonical vortex position field w(z)=x(z)+iy(z), which explicitly breaks the tilt symmetry due to an arbitrary choice of the z-axis, with those of the real physical system recovered in final expression
Theory of Decay of Superfluid Turbulence intheLow-Temperature Limit
We review the theory of relaxational kinetics of superfluid turbulenceâa tangle of quantized vortex linesâin the limit of very low temperatures when the motion of vortices is conservative. While certain important aspects of the decay kinetics depend on whether the tangle is non-structured, like the one corresponding to the Kibble-Zurek picture, or essentially polarized, like the one that emulates the Richardson-Kolmogorov regime of classical turbulence, there are common fundamental features. In both cases, there exists an asymptotic range in the wavenumber space where the energy flux is supported by the cascade of Kelvin waves (kelvons)âprecessing distortions propagating along the vortex filaments. At large enough wavenumbers, the Kelvin-wave cascade is supported by three-kelvon elastic scattering. At zero temperature, the dissipative cutoff of the Kelvin-wave cascade is due to the emission of phonons, in which an elementary process converts two kelvons with almost opposite momenta into one bulk phonon. Along with the standard set of conservation laws, a crucial role in the theory of low-temperature vortex dynamics is played by the fact of integrability of the local induction approximation (LIA) controlled by the parameter Î=lnâ(λ/a 0), with λ the characteristic kelvon wavelength and a 0 the vortex core radius. While excluding a straightforward onset of the pure three-kelvon cascade, the integrability of LIA does not plug the cascade because of the natural availability of the kinetic channels associated with vortex line reconnections. We argue that the crossover from Richardson-Kolmogorov to the Kelvin-wave cascade is due to eventual dominance of local induction of a single line over the collective induction of polarized eddies, which causes the breakdown of classical-fluid regime and gives rise to a reconnection-driven inertial rang
Thermodynamics of the 3D Hubbard model on approach to the Neel transition
We study the thermodynamic properties of the 3D Hubbard model for
temperatures down to the Neel temperature using cluster dynamical mean-field
theory. In particular we calculate the energy, entropy, density, double
occupancy and nearest-neighbor spin correlations as a function of chemical
potential, temperature and repulsion strength. To make contact with cold-gas
experiments, we also compute properties of the system subject to an external
trap in the local density approximation. We find that an entropy per particle
at is sufficient to achieve a Neel state in the
center of the trap, substantially higher than the entropy required in a
homogeneous system. Precursors to antiferromagnetism can clearly be observed in
nearest-neighbor spin correlators.Comment: 4 pages, 6 figure
Diagrammatic Quantum Monte Carlo solution of the two-dimensional Cooperon-Fermion model
We investigate the two-dimensional cooperon-fermion model in the correlated
regime with a new continuous-time diagrammatic determinant quantum Monte Carlo
(DDQMC) algorithm. We estimate the transition temperature , examine the
effectively reduced band gap and cooperon mass, and find that delocalization of
the cooperons enhances the diamagnetism. When applied to diamagnetism of the
pseudogap phase in high- cuprates, we obtain results in a qualitative
agreement with recent torque magnetization measurements.Comment: 8 pages, 11 figure
Identification of Kelvin waves: numerical challenges
Kelvin waves are expected to play an essential role in the energy dissipation
for quantized vortices. However, the identification of these helical
distortions is not straightforward, especially in case of vortex tangle. Here
we review several numerical methods that have been used to identify Kelvin
waves within the vortex filament model. We test their validity using several
examples and estimate whether these methods are accurate enough to verify the
correct Kelvin spectrum. We also illustrate how the correlation dimension is
related to different Kelvin spectra and remind that the 3D energy spectrum E(k)
takes the form 1/k in the high-k region, even in the presence of Kelvin waves.Comment: 6 pages, 5 figures. The final publication is available at
http://www.springerlink.co
Diagrammatic Monte Carlo for Correlated Fermions
We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC)
can be used for tackling hard fermionic quantum many-body problems in the
thermodynamic limit by presenting accurate results for the repulsive Hubbard
model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic
series for the single-particle self-energy we can study moderate values of the
on-site repulsion () and temperatures down to . We
compare our results with high temperature series expansion and with single-site
and cluster dynamical mean-field theory.Comment: 4 pages, 5 figures, stylistic change
On-site number statistics of ultracold lattice bosons
We study on-site occupation number fluctuations in a system of interacting
bosons in an optical lattice. The ground-state distribution is obtained
analytically in the limiting cases of strong and weak interaction, and by means
of exact Monte Carlo simulations in the strongly correlated regime. As the
interaction is increased, the distribution evolves from Poissonian in the
non-interacting gas to a sharply peaked distribution in the Mott-insulator (MI)
regime. In the special case of large occupation numbers, we demonstrate
analytically and check numerically that there exists a wide interval of
interaction strength, in which the on-site number fluctuations remain Gaussian
and are gradually squeezed until they are of order unity near the superfluid
(SF)-MI transition. Recently, the on-site number statistics were studied
experimentally in a wide range of lattice potential depths [Phys. Rev. Lett.
\textbf{96}, 090401 (2006)]. In our simulations, we are able to directly
reproduce experimental conditions using temperature as the only free parameter.
Pronounced temperature dependence suggests that measurements of on-site atom
number fluctuations can be employed as a reliable method of thermometry in both
SF and MI regimes.Comment: 9 pages, 4 figure
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