4,145 research outputs found
A Holographic Path to the Turbulent Side of Gravity
We study the dynamics of a 2+1 dimensional relativistic viscous conformal
fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the
"gravity/fluid correspondence", to 3+1 dimensional asymptotically anti-de
Sitter (AAdS) black brane solutions to the Einstein equation. We examine
stability properties of shear flows, which correspond to hydrodynamic
quasinormal modes of the black brane. We find that, for sufficiently high
Reynolds number, the solution undergoes an inverse turbulent cascade to long
wavelength modes. We then map this fluid solution, via the gravity/fluid
duality, into a bulk metric. This suggests a new and interesting feature of the
behavior of perturbed AAdS black holes and black branes, which is not readily
captured by a standard quasinormal mode analysis. Namely, for sufficiently
large perturbed black objects (with long-lived quasinormal modes), nonlinear
effects transfer energy from short to long wavelength modes via a turbulent
cascade within the metric perturbation. As long wavelength modes have slower
decay, this lengthens the overall lifetime of the perturbation. We also discuss
various implications of this behavior, including expectations for higher
dimensions, and the possibility of predicting turbulence in more general
gravitational scenarios.Comment: 24 pages, 10 figures; v2: references added, and several minor change
Algebraic time-decay for the bipolar quantum hydrodynamic model
The initial value problem is considered in the present paper for bipolar
quantum hydrodynamic model for semiconductors (QHD) in . We prove
that the unique strong solution exists globally in time and tends to the
asymptotical state with an algebraic rate as . And, we show that
the global solution of linearized bipolar QHD system decays in time at an
algebraic decay rate from both above and below. This means in general, we can
not get exponential time-decay rate for bipolar QHD system, which is different
from the case of unipolar QHD model (where global solutions tend to the
equilibrium state at an exponential time-decay rate) and is mainly caused by
the nonlinear coupling and cancelation between two carriers. Moreover, it is
also shown that the nonlinear dispersion does not affect the long time
asymptotic behavior, which by product gives rise to the algebraic time-decay
rate of the solution of the bipolar hydrodynamical model in the semiclassical
limit.Comment: 23 page
Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
Consistent formulations of relativistic viscous hydrodynamics involve short
lived modes, leading to asymptotic rather than convergent gradient expansions.
In this Letter we consider the Mueller-Israel-Stewart theory applied to a
longitudinally expanding quark-gluon plasma system and identify hydrodynamics
as a universal attractor without invoking the gradient expansion. We give
strong evidence for the existence of this attractor and then show that it can
be recovered from the divergent gradient expansion by Borel summation. This
requires careful accounting for the short-lived modes which leads to an
intricate mathematical structure known from the theory of resurgence.Comment: Presentation improved, typos fixed; roughly matches the published
versio
Electromagnetic properties of viscous charged fluids
We provide a general theoretical framework to describe the electromagnetic
properties of viscous charged fluids, consisting for example of electrons in
certain solids or plasmas. We confirm that finite viscosity leads to multiple
modes of evanescent electromagnetic waves at a given frequency, one of which is
characterized by a negative index of refraction, as previously discussed in a
simplified model by one of the authors. In particular we explain how optical
spectroscopy can be used to probe the viscosity. We concentrate on the impact
of this on the coefficients of refraction and reflection at the sample-vacuum
interface. Analytical expressions are obtained relating the viscosity parameter
to the reflection and transmission coefficients of light. We demonstrate that
finite viscosity has the effect to decrease the reflectivity of a metallic
surface, while the electromagnetic field penetrates more deeply. While on a
phenomenological level there are similarities to the anomalous skin effect, the
model presented here requires no particular assumptions regarding the
corpuscular nature of the charge liquid. A striking consequence of the
branching phenomenon into two degenerate modes is the occurrence in a
half-infinite sample of oscillations of the electromagnetic field intensity as
a function of distance from the interface.Comment: 12 pages, 5 figure
Turbulent Black Holes
We show that rapidly-spinning black holes can display turbulent gravitational
behavior which is mediated by a new type of parametric instability. This
instability transfers energy from higher temporal and azimuthal spatial
frequencies to lower frequencies--- a phenomenon reminiscent of the inverse
energy cascade displayed by 2+1-dimensional turbulent fluids. Our finding
reveals a path towards gravitational turbulence for perturbations of
rapidly-spinning black holes, and provides the first evidence for gravitational
turbulence in an asymptotically flat spacetime. Interestingly, this finding
predicts observable gravitational wave signatures from such phenomena in black
hole binaries with high spins and gives a gravitational description of
turbulence relevant to the fluid-gravity duality.Comment: 5+3 pages, 2 figures, corrected an error in the treatment of the
driving mode; example and figures changed, discussion adde
Microscopic dynamics in liquid metals: the experimental point of view
The experimental results relevant for the understanding of the microscopic
dynamics in liquid metals are reviewed, with special regards to the ones
achieved in the last two decades. Inelastic Neutron Scattering played a major
role since the development of neutron facilities in the sixties. The last ten
years, however, saw the development of third generation radiation sources,
which opened the possibility of performing Inelastic Scattering with X rays,
thus disclosing previously unaccessible energy-momentum regions. The purely
coherent response of X rays, moreover, combined with the mixed
coherent/incoherent response typical of neutron scattering, provides enormous
potentialities to disentangle aspects related to the collectivity of motion
from the single particle dynamics.
If the last twenty years saw major experimental developments, on the
theoretical side fresh ideas came up to the side of the most traditional and
established theories. Beside the raw experimental results, therefore, we review
models and theoretical approaches for the description of microscopic dynamics
over different length-scales, from the hydrodynamic region down to the single
particle regime, walking the perilous and sometimes uncharted path of the
generalized hydrodynamics extension. Approaches peculiar of conductive systems,
based on the ionic plasma theory, are also considered, as well as kinetic and
mode coupling theory applied to hard sphere systems, which turn out to mimic
with remarkable detail the atomic dynamics of liquid metals. Finally, cutting
edges issues and open problems, such as the ultimate origin of the anomalous
acoustic dispersion or the relevance of transport properties of a conductive
systems in ruling the ionic dynamic structure factor are discussed.Comment: 53 pages, 41 figures, to appear in "The Review of Modern Physics".
Tentatively scheduled for July issu
Formulating Viscous Hydrodynamics for Large Velocity Gradients
Viscous corrections to relativistic hydrodynamics, which are usually
formulated for small velocity g radients, have recently been extended from
Navier-Stokes formulations to a class of treatments based on Israel-Stewart
equations. Israel-Stewart treatments, which treat the spatial components of the
s tress-energy tensor tau_ij as dynamical objects, introduce new parameters,
such as the relaxati on times describing non-equilibrium behavior of the
elements tau_ij. By considering linear resp onse theory and entropy
constraints, we show how the additional parameters are related to fluctuatio ns
of tau_ij. Furthermore, the Israel-Stewart parameters are analyzed for their
ability to prov ide stable and physical solutions for sound waves. Finally, it
is shown how these parameters, which are naturally described by correlation
functions in real time, might be constrained by lattice calcu lations, which
are based on path-integral formulations in imaginary time.Comment: 16 page
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