193 research outputs found
Inverse spectral problems for Sturm-Liouville operators with singular potentials
The inverse spectral problem is solved for the class of Sturm-Liouville
operators with singular real-valued potentials from the space .
The potential is recovered via the eigenvalues and the corresponding norming
constants. The reconstruction algorithm is presented and its stability proved.
Also, the set of all possible spectral data is explicitly described and the
isospectral sets are characterized.Comment: Submitted to Inverse Problem
How strange are compact star interiors ?
We discuss a Nambu--Jona-Lasinio (NJL) type quantum field theoretical
approach to the quark matter equation of state with color superconductivity and
construct hybrid star models on this basis. It has recently been demonstrated
that with increasing baryon density, the different quark flavors may occur
sequentially, starting with down-quarks only, before the second light quark
flavor and at highest densities also the strange quark flavor appears. We find
that color superconducting phases are favorable over non-superconducting ones
which entails consequences for thermodynamic and transport properties of hybrid
star matter. In particular, for NJL-type models no strange quark matter phases
can occur in compact star interiors due to mechanical instability against
gravitational collapse, unless a sufficiently strong flavor mixing as provided
by the Kobayashi-Maskawa-'t Hooft determinant interaction is present in the
model. We discuss observational data on mass-radius relationships of compact
stars which can put constraints on the properties of dense matter equation of
state.Comment: 7 pages, 2 figures, to appear in the Proceedings of the International
Conference SQM2009, Buzios, Rio de Janeiro, Brazil, Sep.27-Oct.2, 200
An Exact General-Relativity Solution for the Motion and Intersections of Self-Gravitating Shells in the Field of a Massive Black Hole
The motion with intersections of relativistic gravitating shells in the
Schwarzschild gravitational field of a central body is considered. Formulas are
derived for calculating parameters of the shells after intersection via their
parameters before intersection. Such special cases as the Newtonian
approximation, intersections of light shells, and intersections of a test shell
with a gravitating shell are also considered. The ejection of one of the shells
to infinity in the relativistic region is described. The equations of motion
for the shells are analyzed numerically.Comment: 21 pages, 8 figure
The Role of Strangeness in Astrophysics - an Odyssey through Strange Phases
The equation of state for compact stars is reviewed with special emphasis on
the role of strange hadrons, strange dibaryons and strange quark matter.
Implications for the properties of compact stars are presented. The importance
of neutron star data to constrain the properties of hypothetic particles and
the possible existence of exotic phases in dense matter is outlined. We also
discuss the growing interplay between astrophysics and heavy-ion physics.Comment: invited talk given at Strange Quark Matter 2001, Frankfurt, Germany,
8 pages, uses iopart.cls, minor modifications, version to appear in J. Phys.
Periodic Pattern in the Residual-Velocity Field of OB Associations
An analysis of the residual-velocity field of OB associations within 3 kpc of
the Sun has revealed periodic variations in the radial residual velocities
along the Galactic radius vector with a typical scale length of
lambda=2.0(+/-0.2) kpc and a mean amplitude of fR=7(+/-1) km/s. The fact that
the radial residual velocities of almost all OB-associations in rich
stellar-gas complexes are directed toward the Galactic center suggests that the
solar neighborhood under consideration is within the corotation radius. The
azimuthal-velocity field exhibits a distinct periodic pattern in the region
0<l<180 degrees, where the mean azimuthal-velocity amplitude is ft=6(+/-2)
km/s. There is no periodic pattern of the azimuthal-velocity field in the
region 180<l<360 degrees. The locations of the Cygnus arm, as well as the
Perseus arm, inferred from an analysis of the radial- and azimuthal-velocity
fields coincide. The periodic patterns of the residual-velocity fields of
Cepheids and OB associations share many common features.Comment: 21 page
Stellar structure and compact objects before 1940: Towards relativistic astrophysics
Since the mid-1920s, different strands of research used stars as "physics
laboratories" for investigating the nature of matter under extreme densities
and pressures, impossible to realize on Earth. To trace this process this paper
is following the evolution of the concept of a dense core in stars, which was
important both for an understanding of stellar evolution and as a testing
ground for the fast-evolving field of nuclear physics. In spite of the divide
between physicists and astrophysicists, some key actors working in the
cross-fertilized soil of overlapping but different scientific cultures
formulated models and tentative theories that gradually evolved into more
realistic and structured astrophysical objects. These investigations culminated
in the first contact with general relativity in 1939, when J. Robert
Oppenheimer and his students George Volkoff and Hartland Snyder systematically
applied the theory to the dense core of a collapsing neutron star. This
pioneering application of Einstein's theory to an astrophysical compact object
can be regarded as a milestone in the path eventually leading to the emergence
of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal
Compact stars made of fermionic dark matter
Compact stars consisting of fermions with arbitrary masses and interaction
strengths are studied by solving the structure equation of general relativity,
the Tolman-Oppenheimer-Volkoff equations. Scaling solutions are derived for a
free and an interacting Fermi gas and tested by numerical calculations. We
demonstrate that there is a unique mass-radius relation for compact stars made
of free fermions which is independent of the fermion mass. For sufficiently
strong interactions, the maximum stable mass of compact stars and its radius
are controlled by the parameter of the interaction, both increasing linearly
with the interaction strength. The mass-radius relation for compact stars made
of strongly interacting fermions shows that the radius remains approximately
constant for a wide range of compact star masses.Comment: 19 pages, 8 figures, refs. added, version to appear in Physical
Review
Spectral correlations in a random distributed feedback fibre laser
Random distributed feedback fibre lasers belong to the class of random lasers, where the feedback is provided by amplified Rayleigh scattering on sub-micron refractive index inhomogenities randomly distributed over the fibre length. Despite the elastic nature of Rayleigh scattering, the feedback mechanism has been insofar deemed incoherent, which corresponds to the commonly observed smooth generation spectra. Here, using a real-time spectral measurement technique based on a scanning Fabry-PĂ©rot interferometer, we observe long-living narrowband components in the random fibre laser's spectrum. Statistical analysis of the âŒ104 single-scan spectra reveals a preferential interspacing for the components and their anticorrelation in intensities. Furthermore, using mutual information analysis, we confirm the existence of nonlinear correlations between different parts of the random fibre laser spectra. The existence of such narrowband spectral components, together with their observed correlations, establishes a long-missing parallel between the fields of random fibre lasers and conventional random lasers
Gravitational-wave research as an emerging field in the Max Planck Society. The long roots of GEO600 and of the Albert Einstein Institute
On the occasion of the 50th anniversary since the beginning of the search for
gravitational waves at the Max Planck Society, and in coincidence with the 25th
anniversary of the foundation of the Albert Einstein Institute, we explore the
interplay between the renaissance of general relativity and the advent of
relativistic astrophysics following the German early involvement in
gravitational-wave research, to the point when gravitational-wave detection
became established by the appearance of full-scale detectors and international
collaborations. On the background of the spectacular astrophysical discoveries
of the 1960s and the growing role of relativistic astrophysics, Ludwig Biermann
and his collaborators at the Max Planck Institute for Astrophysics in Munich
became deeply involved in research related to such new horizons. At the end of
the 1960s, Joseph Weber's announcements claiming detection of gravitational
waves sparked the decisive entry of this group into the field, in parallel with
the appointment of the renowned relativist Juergen Ehlers. The Munich area
group of Max Planck institutes provided the fertile ground for acquiring a
leading position in the 1970s, facilitating the experimental transition from
resonant bars towards laser interferometry and its innovation at increasingly
large scales, eventually moving to a dedicated site in Hannover in the early
1990s. The Hannover group emphasized perfecting experimental systems at pilot
scales, and never developed a full-sized detector, rather joining the LIGO
Scientific Collaboration at the end of the century. In parallel, the Max Planck
Institute for Gravitational Physics (Albert Einstein Institute) had been
founded in Potsdam, and both sites, in Hannover and Potsdam, became a unified
entity in the early 2000s and were central contributors to the first detection
of gravitational waves in 2015.Comment: 94 pages. Enlarged version including new results from further
archival research. A previous version appears as a chapter in the volume The
Renaissance of General Relativity in Context, edited by A. Blum, R. Lalli and
J. Renn (Boston: Birkhauser, 2020
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