103 research outputs found
Holomorphic Hermite polynomials in two variables
Generalizations of the Hermite polynomials to many variables and/or to the
complex domain have been located in mathematical and physical literature for
some decades. Polynomials traditionally called complex Hermite ones are mostly
understood as polynomials in and which in fact makes them
polynomials in two real variables with complex coefficients. The present paper
proposes to investigate for the first time holomorphic Hermite polynomials in
two variables. Their algebraic and analytic properties are developed here.
While the algebraic properties do not differ too much for those considered so
far, their analytic features are based on a kind of non-rotational
orthogonality invented by van Eijndhoven and Meyers. Inspired by their
invention we merely follow the idea of Bargmann's seminal paper (1961) giving
explicit construction of reproducing kernel Hilbert spaces based on those
polynomials. "Homotopic" behavior of our new formation culminates in comparing
it to the very classical Bargmann space of two variables on one edge and the
aforementioned Hermite polynomials in and on the other. Unlike in
the case of Bargmann's basis our Hermite polynomials are not product ones but
factorize to it when bonded together with the first case of limit properties
leading both to the Bargmann basis and suitable form of the reproducing kernel.
Also in the second limit we recover standard results obeyed by Hermite
polynomials in and
Squeezing: the ups and downs
We present an operator theoretic side of the story of squeezed states
regardless the order of squeezing. For low order, that is for displacement
(order 1) and squeeze (order 2) operators, we bring back to consciousness what
is know or rather what has to be known by making the exposition as exhaustive
as possible. For the order 2 (squeeze) we propose an interesting model of the
Segal-Bargmann type. For higher order the impossibility of squeezing in the
traditional sense is proved rigorously. Nevertheless what we offer is the
state-of-the-art concerning the topic.Comment: 21 pages; improved presentation; it has been published by Proceedings
of the Royal Society
Squeezed States and Hermite polynomials in a Complex Variable
Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec
[J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of
coherent states, related to the Hermite polynomials in a complex variable which
are orthogonal with respect to a non-rotationally invariant measure. We
investigate relations between these coherent states and obtain the relationship
between them and the squeezed states of quantum optics. We also obtain a second
realization of the canonical coherent states in the Bargmann space of analytic
functions, in terms of a squeezed basis. All this is done in the flavor of the
classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page
Absolute dimensions of the unevolved B-type eclipsing binary GG Orionis
We present photometric observations in B and V as well as spectroscopic
observations of the detached, eccentric 6.6-day double-lined eclipsing binary
GG Ori, a member of the Orion OB1 association. Absolute dimensions of the
components, which are virtually identical, are determined to high accuracy
(better than 1% in the masses and better than 2% in the radii) for the purpose
of testing various aspects of theoretical modeling. We obtain M(A) = 2.342 +/-
0.016 solar masses and R(A) = 1.852 +/- 0.025 solar radii for the primary, and
M(B) = 2.338 +/- 0.017 solar masses and R(B) = 1.830 +/- 0.025 solar radii for
the secondary. The effective temperature of both stars is 9950 +/- 200 K,
corresponding to a spectral type of B9.5. GG Ori is very close to the ZAMS, and
comparison with current stellar evolution models gives ages of 65-82 Myr or 7.7
Myr depending on whether the system is considered to be burning hydrogen on the
main sequence or still in the final stages of pre-main sequence contraction. We
have detected apsidal motion in the binary at a rate of dw/dt = 0.00061 +/-
0.00025 degrees per cycle, corresponding to an apsidal period of U = 10700 +/-
4500 yr. A substantial fraction of this (approximately 70%) is due to the
contribution from General Relativity.Comment: To appear in The Astronomical Journal, December 200
A Mediterranean-type diet is associated with better metabolic profile in urban Polish adults: Results from the HAPIEE study
The aim of this study was to evaluate the relationship between adherence to a Mediterranean-type diet and metabolic syndrome (MetS) in the Polish arm of the Health, Alcohol and Psychosocial factors In Eastern Europe (HAPIEE) cohort study
A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as “coherent states” today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Nonclassical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superselection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the seminal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here originated from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics communit
Feature tracking microfluidic analysis reveals differential roles of viscosity and friction in sickle cell blood
Characterization of blood flow rheology in hematological disorders is critical for understanding disease pathophysiology. Existing methods to measure blood rheological parameters are limited in their physiological relevance, and there is a need for new tools that focus on the microcirculation and extract properties at finer resolution than overall flow resistance. Herein, we present a method that combines microfluidic systems and powerful object-tracking computational technologies with mathematical modeling to separate the red blood cell flow profile into a bulk component and a wall component. We use this framework to evaluate differential contributions of effective viscosity and wall friction to the overall resistance in blood from patients with Sickle Cell Disease (SCD) under a range of oxygen tensions. Our results demonstrate that blood from patients with SCD exhibits elevated frictional and viscous resistances at all physiologic oxygen tensions. Additionally, the viscous resistance increases more rapidly than the frictional resistance as oxygen tension decreases, which may confound analyses that extract only flow velocities or overall flow resistances. Furthermore, we evaluate the impact of transfusion treatments on the components of the resistance, revealing patient variability in blood properties that may improve our understanding of the heterogeneity of clinical responses to such treatments. Overall, our system provides a new method to analyze patient-specific blood properties and can be applied to a wide range of hematological and vascular disorders
Proof-of-concept demonstration of edge-illumination x-ray phase contrast imaging combined with tomosynthesis.
In this note we present the first proof-of-concept results on the potential effectiveness of the edge-illumination x-ray phase contrast method (in its 'coded-aperture' based lab implementation) combined with tomosynthesis. We believe that, albeit admittedly preliminary (e.g. we only present phantom work), these results deserve early publication in a note primarily for four reasons. First, we fully modelled the imaging acquisition method, and validated the simulation directly with experimental results. This shows that the implementation of the method in the new geometry is understood, and thus that it will be possible to use the model to simulate more complex scenarios in the future. Secondly, we show that a strong phase contrast signal is preserved in the reconstructed tomosynthesis slices: this was a concern, as the high spatial frequency nature of the signal makes it sensitive to any filtration-related procedure. Third, we show that, despite the non-optimized nature of the imaging prototype used, we can perform a full angular scan at acceptable dose levels and with exposure times not excessively distant from what is required by clinical practice. Finally, we discuss how the proposed phase contrast method, unlike other approaches apart from free-space propagation (which however requires a smaller focal spot, thus reducing the flux and increasing exposure times), can be easily implemented in a tomosynthesis geometry suitable for clinical use. In summary, we find that these technical results indicate a high potential for the combination of the two methods. Combining slice separation with detail enhancement provided by phase effects would substantially increase the detectability of small lesions and/or calcifications, which we aim to demonstrate in the next steps of this study
Edge illumination and coded-aperture X-ray phase-contrast imaging: Increased sensitivity at synchrotrons and lab-based translations into medicine, biology and materials science
The edge illumination principle was first proposed at Elettra (Italy) in the late nineties, as an alternative method for achieving high phase sensitivity with a very simple and flexible set-up, and has since been under continuous development in the radiation physics group at UCL. Edge illumination allows overcoming most of the limitations of other phase-contrast techniques, enabling their translation into a laboratory environment. It is relatively insensitive to mechanical and thermal instabilities and it can be adapted to the divergent and polychromatic beams provided by X-ray tubes. This method has been demonstrated to work efficiently with source sizes up to 100m, compatible with state-of-the-art mammography sources. Two full prototypes have been built and are operational at UCL. Recent activity focused on applications such as breast and cartilage imaging, homeland security and detection of defects in composite materials. New methods such as phase retrieval, tomosynthesis and computed tomography algorithms are currently being theoretically and experimentally investigated. These results strongly indicate the technique as an extremely powerful and versatile tool for X-ray imaging in a wide range of applications
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