5,747 research outputs found
Turbulent flow in graphene
We demonstrate the possibility of a turbulent flow of electrons in graphene
in the hydrodynamic region, by calculating the corresponding turbulent
probability density function. This is used to calculate the contribution of the
turbulent flow to the conductivity within a quantum Boltzmann approach. The
dependence of the conductivity on the system parameters arising from the
turbulent flow is very different from that due to scattering.Comment: 4 pages, Latex file, Journal versio
Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation
By performing two parallel numerical experiments -- solving the dynamical
Hamiltonian equations and solving the Hasselmann kinetic equation -- we
examined the applicability of the theory of weak turbulence to the description
of the time evolution of an ensemble of free surface waves (a swell) on deep
water. We observed qualitative coincidence of the results.
To achieve quantitative coincidence, we augmented the kinetic equation by an
empirical dissipation term modelling the strongly nonlinear process of
white-capping. Fitting the two experiments, we determined the dissipation
function due to wave breaking and found that it depends very sharply on the
parameter of nonlinearity (the surface steepness). The onset of white-capping
can be compared to a second-order phase transition. This result corroborates
with experimental observations by Banner, Babanin, Young.Comment: 5 pages, 5 figures, Submitted in Phys. Rev. Letter
Symmetry Induced 4-Wave Capillary Wave Turbulence
We report theoretical and experimental results on 4-wave capillary wave
turbulence. A system consisting of two inmiscible and incompressible fluids of
the same density can be written in a Hamiltonian way for the conjugated pair
. When given the symmetry , the set of weakly non-linear
interacting waves display a Kolmogorov-Zakharov (KZ) spectrum
in wave vector space. The wave system was studied experimentally with two
inmiscible fluids of almost equal densities (water and silicon oil) where the
capillary surface waves are excited by a low frequency random forcing. The
power spectral density (PSD) and probability density function (PDF) of the
local wave amplitude are studied. Both theoretical and experimental results are
in fairly good agreement with each other.Comment: 6 pages, 2 figure
On the Quantum Kinetic Equation in Weak Turbulence
The quantum kinetic equation used in the study of weak turbulence is
reconsidered in the context of a theory with a generic quartic interaction. The
expectation value of the time derivative of the mode number operators is
computed in a perturbation expansion which places the large diagonal component
of the quartic term in the unperturbed Hamiltonian. Although one is not
perturbing around a free field theory, the calculation is easily tractable
owing to the fact that the unperturbed Hamiltonian can be written solely in
terms of the mode number operators.Comment: 12 pages, LATEX, no figures, to appear in Phys. Rev.
Anomalous mass dependence of radiative quark energy loss in a finite-size quark-gluon plasma
We demonstrate that for a finite-size quark-gluon plasma the induced gluon
radiation from heavy quarks is stronger than that for light quarks when the
gluon formation length becomes comparable with (or exceeds) the size of the
plasma. The effect is due to oscillations of the light-cone wave function for
the in-medium transition. The dead cone model by Dokshitzer and
Kharzeev neglecting quantum finite-size effects is not valid in this regime.
The finite-size effects also enhance the photon emission from heavy quarks.Comment: 8 pages, 3 figure
General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations
We derive the soliton matrices corresponding to an arbitrary number of
higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary
matrix dimension, thus giving the complete solution to the problem of
higher-order solitons. Our soliton matrices explicitly give all higher-order
multi-soliton solutions to the nonlinear partial differential equations
integrable through the matrix Riemann-Hilbert problem. We have applied these
general results to the three-wave interaction system, and derived new classes
of higher-order soliton and two-soliton solutions, in complement to those from
our previous publication [Stud. Appl. Math. \textbf{110}, 297 (2003)], where
only the elementary higher-order zeros were considered. The higher-order
solitons corresponding to non-elementary zeros generically describe the
simultaneous breakup of a pumping wave into the other two components
( and ) and merger of and waves into the pumping
wave. The two-soliton solutions corresponding to two simple zeros generically
describe the breakup of the pumping wave into the and
components, and the reverse process. In the non-generic cases, these
two-soliton solutions could describe the elastic interaction of the and
waves, thus reproducing previous results obtained by Zakharov and Manakov
[Zh. Eksp. Teor. Fiz. \textbf{69}, 1654 (1975)] and Kaup [Stud. Appl. Math.
\textbf{55}, 9 (1976)].Comment: To appear in J. Math. Phy
Partially Massless Spin 2 Electrodynamics
We propose that maximal depth, partially massless, higher spin excitations
can mediate charged matter interactions in a de Sitter universe. The proposal
is motivated by similarities between these theories and their traditional
Maxwell counterpart: their propagation is lightlike and corresponds to the same
Laplacian eigenmodes as the de Sitter photon; they are conformal in four
dimensions; their gauge invariance has a single scalar parameter and actions
can be expressed as squares of single derivative curvature tensors. We examine
this proposal in detail for its simplest spin 2 example. We find that it is
possible to construct a natural and consistent interaction scheme to conserved
vector electromagnetic currents primarily coupled to the helicity 1 partially
massless modes. The resulting current-current single ``partial-photon''
exchange amplitude is the (very unCoulombic) sum of contact and shorter-range
terms, so the partial photon cannot replace the traditional one, but rather
modifies short range electromagnetic interactions. We also write the gauge
invariant fourth-derivative effective actions that might appear as effective
corrections to the model, and their contributions to the tree amplitude are
also obtained.Comment: 15 pages, LaTe
Integrable turbulence generated from modulational instability of cnoidal waves
We study numerically the nonlinear stage of modulational instability (MI) of
cnoidal waves, in the framework of the focusing one-dimensional Nonlinear
Schrodinger (NLS) equation. Cnoidal waves are the exact periodic solutions of
the NLS equation and can be represented as a lattice of overlapping solitons.
MI of these lattices lead to development of "integrable turbulence" [Zakharov
V.E., Stud. Appl. Math. 122, 219-234 (2009)]. We study the major
characteristics of the turbulence for dn-branch of cnoidal waves and
demonstrate how these characteristics depend on the degree of "overlapping"
between the solitons within the cnoidal wave.
Integrable turbulence, that develops from MI of dn-branch of cnoidal waves,
asymptotically approaches to it's stationary state in oscillatory way. During
this process kinetic and potential energies oscillate around their asymptotic
values. The amplitudes of these oscillations decay with time as t^{-a},
1<a<1.5, the phases contain nonlinear phase shift decaying as t^{-1/2}, and the
frequency of the oscillations is equal to the double maximal growth rate of the
MI, s=2g_{max}. In the asymptotic stationary state the ratio of potential to
kinetic energy is equal to -2. The asymptotic PDF of wave amplitudes is close
to Rayleigh distribution for cnoidal waves with strong overlapping, and is
significantly non-Rayleigh one for cnoidal waves with weak overlapping of
solitons. In the latter case the dynamics of the system reduces to two-soliton
collisions, which occur with exponentially small rate and provide up to
two-fold increase in amplitude compared with the original cnoidal wave.Comment: 36 pages, 25 figure
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