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Yang Chen

Publications and source records attributed to Yang Chen.

At least 793 records · Page 44Linked to original sources
arXiv2006

Painleve IV and degenerate Gaussian Unitary Ensembles

We consider those Gaussian Unitary Ensembles where the eigenvalues have prescribed multiplicities, and obtain joint probability density for the eigenvalues. In the simplest case where there is only one multiple eigenvalue t, this leads to orthogonal polynomials with the Hermite weight perturbed by a factor that has a multiple zero at t. We show through a pair of ladder operators, that the diagonal recurrence coefficients satisfy a particular Painleve IV equation for any real multiplicity. If the multiplicity is even they are expressed in terms of the generalized Hermite polynomials, with t as the independent variable.

math-ph↗
arXiv2005

Perturbed Hankel Determinants

In this short note, we compute, for large n the determinant of a class of n x n Hankel matrices, which arise from a smooth perturbation of the Jacobi weight. For this purpose, we employ the same idea used in previous papers, where the unknown determinant, D_n[w_{α,β}h] is compared with the known determinant D_n[w_{α,β}]. Here w_{α,β} is the Jacobi weight and w_{α,β}h, where h=h(x),x\in[-1,1] is strictly positive and real analytic, is the smooth perturbation on the Jacobi weight w_{α,β}(x):=(1-x)^α(1+x)^β. Applying a previously known formula on the distribution function of linear statistics, we compute the large n asymptotics of D_n[w_{α,β}h] and supply a missing constant of the expansion.

math-ph↗
arXiv2005

Highly Clumpy Structure of the Thermal Composite Supernova Remnant 3C391 Unveiled by Chandra

The nature of the internal thermal X-ray emission seen in ``thermal composite" supernova remnants is still uncertain. Chandra observation of the 3C391 shows a southeast-northwest elongated morphology and unveils a highly clumpy structure of the remnant. Detailed spatially resolved spectral analysis for the small-scale features reveals normal metal abundance and uniform temperature for the interior gas. The properties of the hot gas comparatively favor the cloudlet evaporation model as a main mechanism for the ``thermal composite" X-ray appearance, though radiative rim and thermal conduction may also be effective. A faint protrusion is found in Si and S lines out of the southwest radio border.

astro-ph↗
arXiv2005

Narrow Band Chandra X-ray Analysis of Supernova Remnant 3C391

We present the narrow-band and the equivalent width (EW) images of the thermal composite supernova remnant (SNR) 3C391 for the X-ray emission lines of elements Mg, Si, & S using the Chandra ACIS Observational data. These EW images reveal the spatial distribution of the emission of the metal species Mg, Si, & S in the remnant. They have clumpy structure similar to that seen from the broadband diffuse emission, suggesting that they are largely of interstellar origin. We find an interesting finger-like feature protruding outside the southwestern radio border of the remnant, which is somewhat similar to the jet-like Si structure found in the famous SNR Cas A. This feature may possibly be the debris of the jet of ejecta which implies an asymmetrical supernova explosion of a massive progenitor star.

astro-ph↗
arXiv2005

Orthogonal polynomials with discontinuous weights

In this paper we present a brief description of a ladder operator formalism applied to orthogonal polynomials with discontinuous weights. The two coefficient functions, A_n(z) and B_n(z), appearing in the ladder operators satisfy the two fundamental compatibility conditions previously derived for smooth weights. If the weight is a product of an absolutely continuous reference weight w_0 and a standard jump function, then A_n(z) and B_n(z) have apparent simple poles at these jumps. We exemplify the approach by taking w_0 to be the Hermite weight. For this simpler case we derive, without using the compatibility conditions, a pair of difference equations satisfied by the diagonal and off-diagonal recurrence coefficients for a fixed location of the jump. We also derive a pair of Toda evolution equations for the recurrence coefficients which, when combined with the difference equations, yields a particular Painleve IV.

math-ph↗
arXiv2004

A Chandra ACIS view of the Thermal Composite Supernova Remnant 3C391

We present a 60 ks Chandra ACIS-S observation of the thermal composite supernova remnant 3C391. The southeast-northwest elongated morphology is similar to that previously found in radio and X-ray studies. This observation unveils a highly clumpy structure of the remnant. Detailed spatially resolved spectral analysis for the small-scale features reveals that the interior gas is generally of normal metal abundance and has approached or basically reached ionization equilibrium. The hydrogen column density increases from southeast to northwest. Three mechanisms, radiative rim, thermal conduction, and cloudlet evaporation, may all play roles in the X-ray appearance of 3C391 as a "thermal composite" remnant, but there are difficulties with each of them in explaining some physical properties. Comparatively, the cloudlet evaporation model is favored by the main characteristics such as the highly clumpy structure and the uniform temperature and density distribution over most of the remnant. The directly measured postshock temperature also implies a young age, about 4 kyr, for the remnant. The postshock gas pressure derived from the NE and SW rims, which harbor maser spots, is consistent with the estimate for the maser regions. An unresolved X-ray source is observed on the northwest border and its spectrum is best fitted by a power-law.

astro-ph↗
arXiv2003

Supernova Remnant Crossing a Density Jump: A Thin Shell Model

The environments of supernova explosion are often inhomogeneous and there may be jumps in their density structure. We have developed a semi-analytic model under the thin-shell approximation for supernova remnants that evolve crossing a density jump in the ambient medium. The generic evolutionary relations are presented for the blast wave after impacting on a cavity wall, which may be produced by the energetic stellar wind from the supernova progenitor. The relations can also be extended to the case that the blast waves break out from a dense cloud if different density contrast is used. This model is applied to N132D, a well-known cavity-born supernova remnant whose evolution has not yet been quantitively estimated in a cavity scenario due to lack of model formulae, and self-consistent physical parameters are obtained.

astro-ph↗
arXiv2003

The X-ray problem revisited

In this letter we re-visit the X-ray problem. Assuming point interaction between the conduction electrons and the first instantaneously created core-hole, the latter's Green's function can be represented as a Fredholm determinant of certain Wiener-Hopf operators acting on L^2(0,T) with discontinuous symbols. Here the symbols are the local conduction electron Green's function in the frequency domain and T is the time the core-hole spends in the system before removal. In this situation, the classical theory of singular integral equations usually employed in the literature to compute the large T asymptotics of the Fredholm determinant ceased to be applicable. A rigorous theory first put forward in the context of operator theory comes into play and universal constants are found in the aymptotics.

math-ph↗
arXiv2003

Jacobi Polynomials from Compatibility Conditions

We revisit the ladder operators for orthogonal polynomials and re-interpret two supplementary conditions as compatibility conditions of two linear over-determined systems; one involves the variation of the polynomials with respect to the variable z (spectral parameter) and the other a recurrence relation in n (the lattice variable). For the Jacobi weight w(x) = (1-x)^a(1+x)^b, x in [-1,1],we show how to use the compatibility conditions to explicitly determine the recurrence coefficients of the monic Jacobi polynomials.

math.CA↗
arXiv2001

ASCA Observations of the Thermal Composite Supernova Remnant 3C 391

We present the results from ASCA observations of the centrally enhanced supernova remnant 3C 391 (G31.9+0.0). We use the ASCA SIS data to carry out an investigation of the spatial and spectral properties of the X-ray emission from this remnant. The collisional equilibrium ionization and non-equilibrium ionization spectral fits indicate that the hot gas within the remnant has basically reached ionization equilibrium. The variation of the hydrogen column density across the remnant is in agreement with the presence of a molecular cloud to the northwest. The comparisons of hydrogen column and X-ray hardness between the NW and SE portions of the remnant support a scenario in which the SNR has broken out of a dense region into an adjacent region of lower density. The mean density within the SNR is observed to be much lower than the immediate ambient cloud density. This and the centrally brightened X-ray morphology can be explained either by the evaporation of engulfed cloudlets or by a radiative stage of evolution for the remnant.

astro-ph↗
arXiv2000

Small Eigenvalues of Large Hankel Matrices

In this paper we investigate the smallest eigenvalue, denoted as $\la_N,$ of a $(N+1)\times (N+1)$ Hankel or moments matrix, associated with the weight, $w(x)=\exp(-x^{\bt}),x>0,\bt>0$, in the large $N$ limit. Using a previous result, the asymptotics for the polynomials, $P_n(z),z\notin[0,\infty)$, orthonormal with respect to $w,$ which are required in the determination of $\la_N$ are found. Adopting an argument of Szegö the asymptotic behaviour of $\la_N$, for $\bt>1/2$ where the related moment problem is determinate, is derived. This generalises the result given by Szegö for $\bt=1$. It is shown that for $\bt>1/2$ the smallest eigenvalue of the infinite Hankel matrix is zero, while for $0<\bt<1/2$ it is greater then a positive constant. This shows a phase transition in the corresponding Hermitian random matrix model as the parameter $\bt$ varies with $\bt=1/2$ identified as the critical point. The smallest eigenvalue at this point is conjectured.

math.CA↗
arXiv2000

Determinants of Hankel Matrices

The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval.The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics are well known.

math.CA↗
arXiv2000

Chandra Observations of the Crab-like Supernova Remnant G21.5-0.9

Chandra observations of the Crab-like supernova remnant G21.5-0.9 reveal a compact central core and spectral variations indicative of synchrotron burn-off of higher energy electrons in the inner nebula. The central core is slightly extended, perhaps indicating the presence of an inner wind-shock nebula surrounding the pulsar. No pulsations are observed from the central region, yielding an upper limit of ~40% for the pulsed fraction. A faint outer shell may be the first evidence of the expanding ejecta and blast wave formed in the initial explosion, indicating a composite nature for G21.5-0.9.

astro-ph↗
arXiv1999

Small eigenvalues of large Hankel matrices:The indeterminate case

In this paper we characterise the indeterminate case by the eigenvalues of the Hankel matrices being bounded below by a strictly positive constant. An explicit lower bound is given in terms of the orthonormal polynomials and we find expresions for this lower bound in a number of indeterminate moment problems.

math.CA↗
arXiv1999

An analysis of the X-ray emission from the supernova remnant 3C397

The ASCA SIS and the ROSAT PSPC spectral data of the SNR 3C397 are analysed with a two-component non-equilibrium ionization model. Besides, the ASCA SIS0 and SIS1 spectra are also fitted simultaneously in an equilibrium case. The resulting values of the hydrogen column density yield a distance of $\sim8\kpc$ to 3C397. It is found that the hard X-ray emission, containing S and Fe K$α$ lines, arises primarily from the hot component, while most of the soft emission, composed mainly of Mg, Si, Fe L lines, and continuum, is produced by the cool component. The emission measures suggest that the remnant evolves in a cloudy medium and imply that the supernova progenitor might not be a massive early-type star. The cool component is approaching ionization equilibrium. The ages estimated from the ionization parameters and dynamics are all much greater than the previous determination. We restore the X-ray maps using the ASCA SIS data and compare them with the ROSAT HRI and the NRAO VLA Sky Survey (NVSS) 20 cm maps. The morphology with two bright concentrations suggests a bipolar remnant encountering a denser medium in the west.

astro-ph↗
arXiv1998

X-ray Observation and Analysis of The Composite Supernova Remnant G327.1-1.1

Based on the data from the observation of the SNR G327.1-1.1 by ASCA and ROSAT, we find that G327.1-1.1 is a composite remnant with both a nonthermal emission component and a diffuse thermal emission component. The nonthermal component is well fitted by a power-law model with photon index about 2.2. This component is attributed to the emission from the synchrotron nebula powered by an undiscovered central pulsar. The thermal component has a temperature of about 0.4 keV. We attribute it to the emission from the shock-heat swept-up ISM. Its age, explosion energy and density of ambient medium are derived from the observed thermal component. Some charactistics about the synchrotron nebula are also derived. We search for the pulsed signal, but has not found it. The soft X-ray(0.4 - 2 keV) and hard X-ray(2 - 10 keV) images are different, but they both elongate in the SE-NW direction. And this X-ray SE-NW elongation is in positional coincidence with the radio ridge in MOST 843MHz radio map. We present a possibility that the X-ray nonthermal emission mainly come from the trail produced by a quickly moving undiscoverd pulsar, and the long radio ridge is formed when the pulsar is moving out of the boundary of the plerionic structure.

astro-ph↗
arXiv1998

Statistical properties of localisation--delocalisation transition in one dimension

We study a one-dimensional model of disordered electrons (also relevant for random spin chains), which exhibits a delocalisation transition at half-filling. Exact probability distribution functions for the Wigner time and transmission coefficient are calculated. We identify and distinguish those features of probability densities that are due to rare, trapping configurations of the random potential from those which are due to the proximity to the delocalisation transition.

cond-mat.dis-nn↗