1,314 research outputs found
Lowering and raising operators for the free Meixner class of orthogonal polynomials
We compare some properties of the lowering and raising operators for the
classical and free classes of Meixner polynomials on the real line
The Proper Motion of PSR J0205+6449 in 3C 58
We report on sensitive phase-referenced and gated 1.4-GHz VLBI radio
observations of the pulsar PSR J0205+6449 in the young pulsar-wind nebula 3C
58, made in 2007 and 2010. We employed a novel technique where the ~105-m Green
Bank telescope is used simultaneously to obtain single-dish data used to
determine the pulsar's period as well as to obtain the VLBI data, allowing the
VLBI correlation to be gated synchronously with the pulse to increase the
signal-to-noise. The high timing noise of this young pulsar precludes the
determination of the proper motion from the pulsar timing. We derive the
position of the pulsar accurate at the milliarcsecond level, which is
consistent with a re-determined position from the Chandra X-ray observations.
We reject the original tentative optical identification of the pulsar by
Shearer and Neustroev (2008), but rather identify a different optical
counterpart on their images, with R-band magnitude ~24. We also determine an
accurate proper motion for PSR J0205+6449 of (2.3 +- 0.3) mas/yr, corresponding
to a projected velocity of only (35 +- 6) km/s for a distance of 3.2 kpc, at
p.a. -38 deg. This projected velocity is quite low compared to the velocity
dispersion of known pulsars of ~200 km/s. Our measured proper motion does not
suggest any particular kinematic age for the pulsar.Comment: 10 pages, 7 figures; accepted for publication in MNRA
Soliton dual comb in crystalline microresonators
We present a novel compact dual-comb source based on a monolithic optical
crystalline MgF multi-resonator stack. The coherent soliton combs generated
in two microresonators of the stack with the repetition rate of 12.1 GHz and
difference of 1.62 MHz provided after heterodyning a 300 MHz wide
radio-frequency comb. Analogous system can be used for dual-comb spectroscopy,
coherent LIDAR applications and massively parallel optical communications.Comment: 5 pages, 5 figure
Temporal solitons in optical microresonators
Dissipative solitons can emerge in a wide variety of dissipative nonlinear
systems throughout the fields of optics, medicine or biology. Dissipative
solitons can also exist in Kerr-nonlinear optical resonators and rely on the
double balance between parametric gain and resonator loss on the one hand and
nonlinearity and diffraction or dispersion on the other hand. Mathematically
these solitons are solution to the Lugiato-Lefever equation and exist on top of
a continuous wave (cw) background. Here we report the observation of temporal
dissipative solitons in a high-Q optical microresonator. The solitons are
spontaneously generated when the pump laser is tuned through the effective zero
detuning point of a high-Q resonance, leading to an effective red-detuned
pumping. Red-detuned pumping marks a fundamentally new operating regime in
nonlinear microresonators. While usually unstablethis regime acquires unique
stability in the presence of solitons without any active feedback on the
system. The number of solitons in the resonator can be controlled via the pump
laser detuning and transitions to and between soliton states are associated
with discontinuous steps in the resonator transmission. Beyond enabling to
study soliton physics such as soliton crystals our observations open the route
towards compact, high repetition-rate femto-second sources, where the operating
wavelength is not bound to the availability of broadband laser gain media. The
single soliton states correspond in the frequency domain to low-noise optical
frequency combs with smooth spectral envelopes, critical to applications in
broadband spectroscopy, telecommunications, astronomy and low phase-noise
microwave generation.Comment: Includes Supplementary Informatio
Meixner class of non-commutative generalized stochastic processes with freely independent values I. A characterization
Let be an underlying space with a non-atomic measure on it (e.g.
and is the Lebesgue measure). We introduce and study a
class of non-commutative generalized stochastic processes, indexed by points of
, with freely independent values. Such a process (field),
, , is given a rigorous meaning through smearing out
with test functions on , with being a
(bounded) linear operator in a full Fock space. We define a set
of all continuous polynomials of , and then define a con-commutative
-space by taking the closure of in the norm
, where is the vacuum in the Fock
space. Through procedure of orthogonalization of polynomials, we construct a
unitary isomorphism between and a (Fock-space-type) Hilbert space
, with
explicitly given measures . We identify the Meixner class as those
processes for which the procedure of orthogonalization leaves the set invariant. (Note that, in the general case, the projection of a
continuous monomial of oder onto the -th chaos need not remain a
continuous polynomial.) Each element of the Meixner class is characterized by
two continuous functions and on , such that, in the
space, has representation
\omega(t)=\di_t^\dag+\lambda(t)\di_t^\dag\di_t+\di_t+\eta(t)\di_t^\dag\di^2_t,
where \di_t^\dag and \di_t are the usual creation and annihilation
operators at point
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