246 research outputs found
Integer and fractionalized vortex lattices and off-diagonal long-range order
We analyze the implication of off-diagonal long-range order (ODLRO) for inhomogeneous periodic
field configurations and multi-component order parameters. For single component order parameters
we show that the only static, periodic field configuration consistent with ODLRO is a vortex lattice
with integer flux in units of the flux quantum in each unit cell. For a superconductor with g degenerate
components, fractional vortices are allowed. Depending on the precise order-parameter manifold,
they tend to occur in units of 1/g of the flux quantum. These results are well known to emerge from
the Ginzburg-Landau or BCS theories of superconductivity. Our results imply that they are valid even
if these theories no-longer apply. Integer and fractional vortex lattices are transparently seen to emerge
as a consequence of the macroscopic coherence and single valuedness of the condensat
Core-Collapse Supernovae: Modeling between Pragmatism and Perfectionism
We briefly summarize recent efforts in Garching for modeling stellar core
collapse and post-bounce evolution in one and two dimensions. The transport of
neutrinos of all flavors is treated by iteratively solving the coupled system
of frequency-dependent moment equations together with a model Boltzmann
equation which provides the closure. A variety of progenitor stars, different
nuclear equations of state, stellar rotation, and global asymmetries due to
large-mode hydrodynamic instabilities have been investigated to ascertain the
road to finally successful, convectively supported neutrino-driven explosions.Comment: 8 pages, contribution to Procs. 12th Workshop on Nuclear
Astrophysics, Ringberg Castle, March 22-27, 200
From Dual Unitarity to Generic Quantum Operator Spreading
Dual-unitary circuits are paradigmatic examples of exactly solvable yet
chaotic quantum many-body systems, but solvability naturally goes along with a
degree of non-generic behaviour. By investigating the effect of weakly broken
dual-unitarity on the spreading of local operators we study whether, and how,
small deviations from dual-unitarity recover fully generic many-body dynamics.
We present a discrete path-integral formula for the out-of-time-order
correlator and use it to recover a butterfly velocity smaller than the
light-cone velocity, , and a diffusively broadening operator
front, two generic features of ergodic quantum spin chains absent in
dual-unitary circuit dynamics. We find that the butterfly velocity and
diffusion constant are determined by a small set of microscopic quantities and
that the operator entanglement of the gates plays a crucial role.Comment: (6+17) pages, 5 figures Accepted versio
Conservative formulations of general relativistic kinetic theory
Experience with core-collapse supernova simulations shows that accurate
accounting of total particle number and 4-momentum can be a challenge for
computational radiative transfer. This accurate accounting would be facilitated
by the use of particle number and 4-momentum transport equations that allow
transparent conversion between volume and surface integrals in both
configuration and momentum space. Such conservative formulations of general
relativistic kinetic theory in multiple spatial dimensions are presented in
this paper, and their relevance to core-collapse supernova simulations is
described.Comment: 48 page
Supernova Simulations with Boltzmann Neutrino Transport: A Comparison of Methods
Accurate neutrino transport has been built into spherically symmetric
simulations of stellar core collapse and postbounce evolution. The results of
such simulations agree that spherically symmetric models with standard
microphysical input fail to explode by the delayed, neutrino-driven mechanism.
Independent groups implemented fundamentally different numerical methods to
tackle the Boltzmann neutrino transport equation. Here we present a direct and
detailed comparison of such neutrino radiation-hydrodynamical simulations for
two codes, Agile-Boltztran of the Oak Ridge-Basel group and Vertex of the
Garching group. The former solves the Boltzmann equation directly by an
implicit, general relativistic discrete angle method on the adaptive grid of a
conservative implicit hydrodynamics code with second-order TVD advection. In
contrast, the latter couples a variable Eddington factor technique with an
explicit, moving-grid, conservative high-order Riemann solver with important
relativistic effects treated by an effective gravitational potential. The
presented study is meant to test both neutrino radiation-hydrodynamics
implementations and to provide a data basis for comparisons and verifications
of supernova codes to be developed in the future. Results are discussed for
simulations of the core collapse and post-bounce evolution of a 13 solar mass
star with Newtonian gravity and a 15 solar mass star with relativistic gravity.Comment: 23 pages, 13 figures, revised version, to appear in Ap
Protoneutron star dynamos and pulsar magnetism
We have investigated the turbulent mean-field dynamo action in protoneutron
stars that are subject to convective and neutron finger instabilities during
the early evolutionary phase. While the first one develops mostly in the inner
regions of the star, the second one is favored in the outer regions, where the
Rossby number is much smaller and a mean-field dynamo action is more efficient.
By solving the mean-field induction equation we have computed the critical spin
period below which no dynamo action is possible and found it to be s
for a wide range of stellar models and for both axisymmetric and
non-axisymmetric magnetic fields. Because this critical period is substantially
longer than the characteristic spin period of very young pulsars, we expect
that a mean-field dynamo will be effective for most protoneutron stars. The
saturation dipole field estimated by making use of the model of ``global''
quenching fits well the pulsar magnetic fields inferred from the spin-down
data. Apart from the large scale magnetic field, our model predicts also a
generation of small scale fields which are typically stronger than the poloidal
field and can survive during the lifetime of pulsars. Extremely rapidly
rotating protoneutron stars ( ms) may have the dipole field G.Comment: 7 pages, 6 figures, to appear on A&
Differential Rotation in Neutron Stars: Magnetic Braking and Viscous Damping
Diffferentially rotating stars can support significantly more mass in
equilibrium than nonrotating or uniformly rotating stars, according to general
relativity. The remnant of a binary neutron star merger may give rise to such a
``hypermassive'' object. While such a star may be dynamically stable against
gravitational collapse and bar formation, the radial stabilization due to
differential rotation is likely to be temporary. Magnetic braking and viscosity
combine to drive the star to uniform rotation, even if the seed magnetic field
and the viscosity are small. This process inevitably leads to delayed collapse,
which will be accompanied by a delayed gravitational wave burst and, possibly,
a gamma-ray burst. We provide a simple, Newtonian, MHD calculation of the
braking of differential rotation by magnetic fields and viscosity. The star is
idealized as a differentially rotating, infinite cylinder consisting of a
homogeneous, incompressible conducting gas. We solve analytically the simplest
case in which the gas has no viscosity and the star resides in an exterior
vacuum. We treat numerically cases in which the gas has internal viscosity and
the star is embedded in an exterior, low-density, conducting medium. Our
evolution calculations are presented to stimulate more realistic MHD
simulations in full 3+1 general relativity. They serve to identify some of the
key physical and numerical parameters, scaling behavior and competing
timescales that characterize this important process.Comment: 11 pages. To appear in ApJ (November 20, 2000
Gravitational waves from relativistic rotational core collapse
We present results from simulations of axisymmetric relativistic rotational
core collapse. The general relativistic hydrodynamic equations are formulated
in flux-conservative form and solved using a high-resolution shock-capturing
scheme. The Einstein equations are approximated with a conformally flat
3-metric. We use the quadrupole formula to extract waveforms of the
gravitational radiation emitted during the collapse. A comparison of our
results with those of Newtonian simulations shows that the wave amplitudes
agree within 30%. Surprisingly, in some cases, relativistic effects actually
diminish the amplitude of the gravitational wave signal. We further find that
the parameter range of models suffering multiple coherent bounces due to
centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure
General-Relativistic MHD for the Numerical Construction of Dynamical Spacetimes
We assemble the equations of general relativistic magnetohydrodynamics (MHD)
in 3+1 form. These consist of the complete coupled set of Maxwell equations for
the electromagnetic field, Einstein's equations for the gravitational field,
and the equations of relativistic MHD for a perfectly conducting ideal gas. The
adopted form of the equations is suitable for evolving numerically a
relativistic MHD fluid in a dynamical spacetime characterized by a strong
gravitational field.Comment: 8 pages; scheduled for March 10 issue of Ap
- …