2,990 research outputs found
The double-Kerr equilibrium configurations involving one extreme object
We demonstrate the existence of equilibrium states in the limiting cases of
the double-Kerr solution when one of the constituents is an extreme object. In
the `extreme-subextreme' case the negative mass of one of the constituents is
required for the balance, whereas in the `extreme-superextreme' equilibrium
configurations both Kerr particles may have positive masses. We also show that
the well-known relation |J|=M^2 between the mass and angular momentum in the
extreme single Kerr solution ceases to be a characteristic property of the
extreme Kerr particle in a binary system.Comment: 12 pages, 3 figures, submitted to Class. Quantum Gra
Tomographic entropy and cosmology
The probability representation of quantum mechanics including propagators and
tomograms of quantum states of the universe and its application to quantum
gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator,
free pointlike particle and repulsive oscillator are considered. The notion of
tomographic entropy and its properties are used to find some inequalities for
the tomographic probability determining the quantum state of the universe. The
sense of the inequality as a lower bound for the entropy is clarified.Comment: 19 page
Determining parameters of the Neugebauer family of vacuum spacetimes in terms of data specified on the symmetry axis
We express the complex potential E and the metrical fields omega and gamma of
all stationary axisymmetric vacuum spacetimes that result from the application
of two successive quadruple-Neugebauer (or two double-Harrison) transformations
to Minkowski space in terms of data specified on the symmetry axis, which are
in turn easily expressed in terms of multipole moments. Moreover, we suggest
how, in future papers, we shall apply our approach to do the same thing for
those vacuum solutions that arise from the application of more than two
successive transformations, and for those electrovac solutions that have axis
data similar to that of the vacuum solutions of the Neugebauer family.
(References revised following response from referee.)Comment: 18 pages (REVTEX
Schwarzschild black hole levitating in the hyperextreme Kerr field
The equilibrium configurations between a Schwarzschild black hole and a
hyperextreme Kerr object are shown to be described by a three-parameter
subfamily of the extended double-Kerr solution. For this subfamily, its Ernst
potential and corresponding metric functions, we provide a physical
representation which employs as arbitrary parameters the individual Komar
masses and relative coordinate distance between the sources. The calculation of
horizon's local angular velocity induced in the Schwarzschild black hole by the
Kerr constituent yields a simple expression inversely proportional to the
square of the distance parameter.Comment: 6 pages, 1 figure; improved versio
Nonlinear coherent loss for generating non-classical states
Here we discuss generation of non-classical states of bosonic mode with the
help of artificially designed loss, namely the nonlinear coherent loss. We show
how to generate superpositions of Fock states, and how it is possible to "comb"
the initial states leaving only states with certain properties in the resulting
superposition (for example, a generation of a superposition of Fock states with
odd number of particles). We discuss purity of generated states and estimate
maximal achievable generation fidelity
The double-Reissner-Nordstrom solution and the interaction force between two spherically symmetric charged particles
The physical representation of the general double-Reissner-Nordstrom solution
is obtained by rewriting the N=2 Breton-Manko-Aguilar electrostatic solution in
the Varzugin-Chistyakov parametrization (M_i, Q_i, R). A concise analytical
formula is derived for the interaction force between two arbitrary
Reissner-Nordstrom constituents, and an example of the equilibrium
configuration involving two oppositely charged particles which confirms earlier
Bonnor's prediction of the existence of such configurations is given.Comment: 14 pages, 1 figure; submitted to Physical Review
A pedagogical presentation of a -algebraic approach to quantum tomography
It is now well established that quantum tomography provides an alternative
picture of quantum mechanics. It is common to introduce tomographic concepts
starting with the Schrodinger-Dirac picture of quantum mechanics on Hilbert
spaces. In this picture states are a primary concept and observables are
derived from them. On the other hand, the Heisenberg picture,which has evolved
in the algebraic approach to quantum mechanics, starts with the
algebra of observables and introduce states as a derived concept. The
equivalence between these two pictures amounts essentially, to the
Gelfand-Naimark-Segal construction. In this construction, the abstract algebra is realized as an algebra of operators acting on a constructed
Hilbert space. The representation one defines may be reducible or irreducible,
but in either case it allows to identify an unitary group associated with the
algebra by means of its invertible elements. In this picture both
states and observables are appropriate functions on the group, it follows that
also quantum tomograms are strictly related with appropriate functions
(positive-type)on the group. In this paper we present, by means of very simple
examples, the tomographic description emerging from the set of ideas connected
with the algebra picture of quantum mechanics. In particular, the
tomographic probability distributions are introduced for finite and compact
groups and an autonomous criterion to recognize a given probability
distribution as a tomogram of quantum state is formulated
Statistical analysis of self-similar behaviour in the shear induced melting model
The analysis of the system behavior under the effect of the additive noises
has been done using a simple model of shear melting. The situation with low
intensity of the order parameter noise has been investigated in detail, and
time dependence of the order parameter has been calculated. A distinctive
feature of the obtained dependence is power-law distribution and
self-similarity. The generalized Hurst exponent of the time series has been
found within multifractal detrended fluctuation analysis. It is shown that the
self-similarity of the time series increases when the noise intensity reduces.Comment: 11 pages, 9 figures, 29 reference
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