31 research outputs found
Relativistic bulk viscous fluids of Burgers type and their presence in neutron stars
It is well known that a mixture of two chemical components undergoing one
chemical reaction is a bulk viscous fluid, where the bulk stress evolves
according to the Israel-Stewart theory. Here, we show that a mixture of three
independent chemical components undergoing two distinct chemical reactions can
also be viewed as a bulk viscous fluid, whose bulk stress now is governed by a
second-order differential equation which reproduces the Burgers model for
viscoelasticity. This is a rigorous and physically motivated example of a fluid
model where the viscous stress does not undergo simple Maxwell-Cattaneo
relaxation, and can actually overshoot the Navier-Stokes stress. We show that,
if one accounts for muons, neutron star matter is indeed a bulk viscous fluid
of Burgers type.Comment: 10 pages, 1 figure, published on CQG, see
https://iopscience.iop.org/article/10.1088/1361-6382/ace58
The regime of applicability of Israel-Stewart hydrodynamics
Using analytical tools from linear response theory, we systematically assess
the accuracy of several microscopic derivations of Israel-Stewart hydrodynamics
near local equilibrium. This allows us to "rank" the different approaches in
decreasing order of accuracy as follows: IReD, DNMR, second-order gradient
expansion, and 14-moment approximation. We find that IReD theory is far
superior to Navier-Stokes, being very accurate both in the asymptotic regime
(i.e. for slow processes) and in the transient regime (i.e. on timescales
comparable to the relaxation time). Also, the high accuracy of DNMR is
confirmed, but neglecting second-order terms in the Knudsen number, which would
render the equations parabolic, introduces serious systematic errors. Finally,
second-order gradient expansion (a.k.a. non-resummed BRSSS) is shown to be more
inaccurate than Navier-Stokes in the transient regime. Overall, this analysis
clearly shows that Israel-Stewart hydrodynamics is falsifiable, and the
relaxation time is observable, thereby ending the debate on the viability of
transient hydrodynamics as a well-defined physical theory distinguished from
Navier-Stokes.Comment: 17 pages, 10 figure
A universal formula for the relativistic correction to the mutual friction coupling time-scale in neutron stars
Vortex-mediated mutual friction governs the coupling between the superfluid
and normal components in neutron star interiors. By, for example, comparing
precise timing observations of pulsar glitches with theoretical predictions it
is possible to constrain the physics in the interior of the star, but to do so
an accurate model of the mutual friction coupling in general relativity is
needed. We derive such a model directly from Carter's multifluid formalism, and
study the vortex structure and coupling time-scale between the components in a
relativistic star. We calculate how general relativity modifies the shape and
the density of the quantized vortices and show that, in the quasi-Schwarzschild
coordinates, they can be approximated as straight lines for realistic neutron
star configurations. Finally, we present a simple universal formula (given as a
function of the stellar compactness alone) for the relativistic correction to
the glitch rise-time, which is valid under the assumption that the superfluid
reservoir is in a thin shell in the crust or in the outer core. This universal
relation can be easily employed to correct, a posteriori, any Newtonian
estimate for the coupling time-scale, without any additional computational
expense.Comment: 20 pages, 7 figure
Subluminality of relativistic quantum tunneling
We prove that the classical Dirac equation in the presence of an external
(nondynamical) electromagnetic field is a relativistically causal theory. As a
corollary, we show that it is impossible to use quantum tunneling to transmit
particles or information faster than light. When an electron tunnels through a
barrier, it is bound to remain within its future light cone. In conclusion, the
relativistic quantum tunneling (if modeled using the Dirac equation) is an
entirely subluminal process, and it is not instantaneous.Comment: 14 pages, 6 figures, published on PRA (see
https://doi.org/10.1103/PhysRevA.107.032209
Stability of multi-component Israel-Stewart-Maxwell theory for charge diffusion
We obtain stability criteria for diffusive inviscid multi-component
Israel-Stewart hydrodynamics with and without background or dynamic
electromagnetic fields. Our analysis is grounded on the maximum entropy
principle, and it provides stability conditions that are valid around all
thermodynamic equilibria, including rotating equilibria, charged equilibria,
and equilibria in a background gravitational field. We prove that the
electromagnetic part of the information current is stable and causal by
construction and, therefore, the stability criteria found for Israel-Stewart
theories of hydrodynamics automatically extend to similar formulations of
magnetohydrodynamics.Comment: 14 pages, 0 figures, comments welcome
Relativistic hydrodynamic fluctuations from an effective action: causality, stability, and the information current
Causality is necessary for retarded Green's functions to remain retarded in
all inertial frames in relativity, which ensures that dissipation of
fluctuations is a Lorentz invariant concept. For first-order BDNK theories with
stochastic fluctuations, introduced via the Schwinger-Keldysh formalism, we
show that imposing causality and stability leads to correlation functions of
hydrodynamic fluctuations that only display the expected physical properties at
small frequencies and wavenumber, i.e., within the expected regime of validity
of the first-order approach. For second-order theories of Israel and Stewart
type, constructed using the information current such that entropy production is
always non-negative, a stochastic formulation is presented using the
Martin-Siggia-Rose approach where imposing causality and stability leads to
correlators with the desired properties. We also show how Green's functions can
be determined from such an action. We identify a symmetry,
analogous to the Kubo-Martin-Schwinger symmetry, under which this
Martin-Siggia-Rose action is invariant. This modified Kubo-Martin-Schwinger
symmetry provides a new guide for the effective action formulation of
hydrodynamic systems with dynamics not solely governed by conservation laws.
Furthermore, this symmetry ensures that the principle of detailed balance is
valid in a covariant manner. We employ the new symmetry to further clarify the
connection between the Schwinger-Keldysh and Martin-Siggia-Rose approaches,
establishing a precise link between these descriptions in second-order theories
of relativistic hydrodynamics. Finally, the modified Kubo-Martin-Schwinger
symmetry is used to determine the corresponding action describing diffusion in
Israel-Stewart theories in a general hydrodynamic frame.Comment: 28 page