1,175 research outputs found
QPOs: Einstein's gravity non-linear resonances
There is strong evidence that the observed kHz Quasi Periodic Oscillations
(QPOs) in the X-ray flux of neutron star and black hole sources in LMXRBs are
linked to Einstein's General Relativity. Abramowicz&Klu\'zniak (2001) suggested
a non-linear resonance model to explain the QPOs origin: here we summarize
their idea and the development of a mathematical toy-model which begins to
throw light on the nature of Einstein's gravity non-linear oscillations.Comment: Proceeding of the Einstein's Legacy, Munich 200
A new model for QPOs in accreting black holes: application to the microquasar GRS 1915+105
(abridged) In this paper we extend the idea suggested previously by Petri
(2005a,b) that the high frequency quasi-periodic oscillations observed in
low-mass X-ray binaries may be explained as a resonant oscillation of the
accretion disk with a rotating asymmetric background (gravitational or
magnetic) field imposed by the compact object. Here, we apply this general idea
to black hole binaries. It is assumed that a test particle experiences a
similar parametric resonance mechanism such as the one described in paper I and
II but now the resonance is induced by the interaction between a spiral density
wave in the accretion disk, excited close to the innermost stable circular
orbit, and vertical epicyclic oscillations. We use the Kerr spacetime geometry
to deduce the characteristic frequencies of this test particle. The response of
the test particle is maximal when the frequency ratio of the two strongest
resonances is equal to 3:2 as observed in black hole candidates. Finally,
applying our model to the microquasar GRS 1915+105, we reproduce the correct
value of several HF-QPOs. Indeed the presence of the 168/113/56/42/28 Hz
features in the power spectrum time analysis is predicted. Moreover, based only
on the two HF-QPO frequencies, our model is able to constrain the mass and angular momentum of the accreting black hole.Comment: Accepted for publication in Astrophysics & Space Scienc
Well-posedness of Hydrodynamics on the Moving Elastic Surface
The dynamics of a membrane is a coupled system comprising a moving elastic
surface and an incompressible membrane fluid. We will consider a reduced
elastic surface model, which involves the evolution equations of the moving
surface, the dynamic equations of the two-dimensional fluid, and the
incompressible equation, all of which operate within a curved geometry. In this
paper, we prove the local existence and uniqueness of the solution to the
reduced elastic surface model by reformulating the model into a new system in
the isothermal coordinates. One major difficulty is that of constructing an
appropriate iterative scheme such that the limit system is consistent with the
original system.Comment: The introduction is rewritte
Modulational Instability in Equations of KdV Type
It is a matter of experience that nonlinear waves in dispersive media,
propagating primarily in one direction, may appear periodic in small space and
time scales, but their characteristics --- amplitude, phase, wave number, etc.
--- slowly vary in large space and time scales. In the 1970's, Whitham
developed an asymptotic (WKB) method to study the effects of small
"modulations" on nonlinear periodic wave trains. Since then, there has been a
great deal of work aiming at rigorously justifying the predictions from
Whitham's formal theory. We discuss recent advances in the mathematical
understanding of the dynamics, in particular, the instability of slowly
modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic
Index theory of one dimensional quantum walks and cellular automata
If a one-dimensional quantum lattice system is subject to one step of a
reversible discrete-time dynamics, it is intuitive that as much "quantum
information" as moves into any given block of cells from the left, has to exit
that block to the right. For two types of such systems - namely quantum walks
and cellular automata - we make this intuition precise by defining an index, a
quantity that measures the "net flow of quantum information" through the
system. The index supplies a complete characterization of two properties of the
discrete dynamics. First, two systems S_1, S_2 can be pieced together, in the
sense that there is a system S which locally acts like S_1 in one region and
like S_2 in some other region, if and only if S_1 and S_2 have the same index.
Second, the index labels connected components of such systems: equality of the
index is necessary and sufficient for the existence of a continuous deformation
of S_1 into S_2. In the case of quantum walks, the index is integer-valued,
whereas for cellular automata, it takes values in the group of positive
rationals. In both cases, the map S -> ind S is a group homomorphism if
composition of the discrete dynamics is taken as the group law of the quantum
systems. Systems with trivial index are precisely those which can be realized
by partitioned unitaries, and the prototypes of systems with non-trivial index
are shifts.Comment: 38 pages. v2: added examples, terminology clarifie
Fast variability from black-hole binaries
Currently available information on fast variability of the X-ray emission
from accreting collapsed objects constitutes a complex phenomenology which is
difficult to interpret. We review the current observational standpoint for
black-hole binaries and survey models that have been proposed to interpret it.
Despite the complex structure of the accretion flow, key observational
diagnostics have been identified which can provide direct access to the
dynamics of matter motions in the close vicinity of black holes and thus to the
some of fundamental properties of curved spacetimes, where strong-field general
relativistic effects can be observed.Comment: 20 pages, 11 figures. Accepted for publication in Space Science
Reviews. Also to appear in hard cover in the Space Sciences Series of ISSI
"The Physics of Accretion onto Black Holes" (Springer Publisher
Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point
We consider the Farey fraction spin chain in an external field . Using
ideas from dynamical systems and functional analysis, we show that the free
energy in the vicinity of the second-order phase transition is given,
exactly, by
Here is a reduced
temperature, so that the deviation from the critical point is scaled by the
Lyapunov exponent of the Gauss map, . It follows that
determines the amplitude of both the specific heat and susceptibility
singularities. To our knowledge, there is only one other microscopically
defined interacting model for which the free energy near a phase transition is
known as a function of two variables.
Our results confirm what was found previously with a cluster approximation,
and show that a clustering mechanism is in fact responsible for the transition.
However, the results disagree in part with a renormalisation group treatment
A scalable quantum computer with an ultranarrow optical transition of ultracold neutral atoms in an optical lattice
We propose a new quantum-computing scheme using ultracold neutral ytterbium
atoms in an optical lattice. The nuclear Zeeman sublevels define a qubit. This
choice avoids the natural phase evolution due to the magnetic dipole
interaction between qubits. The Zeeman sublevels with large magnetic moments in
the long-lived metastable state are also exploited to address individual atoms
and to construct a controlled-multiqubit gate. Estimated parameters required
for this scheme show that this proposal is scalable and experimentally
feasible.Comment: 6 pages, 6 figure
Magnetization plateaux in dimerized spin ladder arrays
We investigate the ground state magnetization plateaux appearing in spin 1/2
two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and
dimerized zig-zag interchain couplings. Using both Abelian bosonization and
Lanczos methods we find that the system yields rather unusual plateaux and
exhibits massive and massless phases for specific choices or ``tuning'' of
exchange interactions. The relevance of this behavior in the study of
NH_4CuCl_3 is discussed.Comment: 9 pages, RevTeX, 11 postscript figure
Elementary vortex pinning potential in a chiral p-wave superconductor
The elementary vortex pinning potential is studied in a chiral p-wave
superconductor with a pairing d=z(k_x + i k_y) on the basis of the
quasiclassical theory of superconductivity. An analytical investigation and
numerical results are presented to show that the vortex pinning potential is
dependent on whether the vorticity and chirality are parallel or antiparallel.
Mutual cancellation of the vorticity and chirality around a vortex is
physically crucial to the effect of the pinning center inside the vortex core.Comment: 4 pages, 4 figures include
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