Layer Potential Techniques in Spectral Analysis. Part II: Sensitivity Analysis of Spectral Properties of High Contrast Band‐Gap Materials

2006 ◽  
Vol 5 (2) ◽  
pp. 646-663 ◽  
Author(s):  
Habib Ammari ◽  
Hyeoenbae Kang ◽  
Sofiane Soussi ◽  
Habib Zribi
Keyword(s):  
Sensitivity Analysis ◽  
Spectral Analysis ◽  
Band Gap ◽  
Spectral Properties ◽  
High Contrast ◽  
Layer Potential

scholarly journals On Spectral Properties of Compact Toeplitz Operators on Bergman Space with Logarithmically Decaying Symbol and Applications to Banded Matrices

2021 ◽  
Author(s):  
Mahamet Koïta ◽  
Stanislas Kupin ◽  
Sergey Naboko ◽  
Belco Touré
Keyword(s):  
Spectral Analysis ◽  
Continuous Function ◽  
Bergman Space ◽  
Orthogonal Projection ◽  
Spectral Properties ◽  
Toeplitz Operators ◽  
Closed Subspace ◽  
Jacobi Matrices ◽  
Banded Matrices ◽  
Eigen Values

Abstract Let $L^2({{\mathbb{D}}})$ be the space of measurable square-summable functions on the unit disk. Let $L^2_a({{\mathbb{D}}})$ be the Bergman space, that is, the (closed) subspace of analytic functions in $L^2({{\mathbb{D}}})$. $P_+$ stays for the orthogonal projection going from $L^2({{\mathbb{D}}})$ to $L^2_a({{\mathbb{D}}})$. For a function $\varphi \in L^\infty ({{\mathbb{D}}})$, the Toeplitz operator $T_\varphi : L^2_a({{\mathbb{D}}})\to L^2_a({{\mathbb{D}}})$ is defined as $$\begin{align*} & T_\varphi f=P_+\varphi f, \quad f\in L^2_a({{\mathbb{D}}}). \end{align*}$$The main result of this article are spectral asymptotics for singular (or eigen-) values of compact Toeplitz operators with logarithmically decaying symbols, that is, $$\begin{align*} & \varphi(z)=\varphi_1(e^{i\theta})\, (1+\log(1/(1-r)))^{-\gamma},\quad \gamma>0, \end{align*}$$where $z=re^{i\theta }$ and $\varphi _1$ is a continuous (or piece-wise continuous) function on the unit circle. The result is applied to the spectral analysis of banded (including Jacobi) matrices.

scholarly journals Magnetar X-ray emission mechanisms

2012 ◽  
Vol 8 (S291) ◽  
pp. 160-160
Author(s):  
Silvia Zane
Keyword(s):  
Spectral Analysis ◽  
Physical Interpretation ◽  
Spectral Properties ◽  
Gamma Ray ◽  
X Ray ◽  
Spectral Components ◽  
Self Consistent ◽  
Photon Index ◽  
Index 2 ◽  
Surface Fields

AbstractSoft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are peculiar X-ray sources which are believed to be magnetars: ultra-magnetized neutron stars which emission is dominated by surface fields (often in excess of 1E14 G, i.e. well above the QED threshold).Spectral analysis is an important tool in magnetar astrophysics since it can provide key information on the emission mechanisms. The first attempts at modelling the persistent (i.e. outside bursts) soft X-ray (¡10 keV) spectra of AXPs proved that a model consisting of a blackbody (kT 0.3-0.6 keV) plus a power-law (photon index 2-4) could successfully reproduce the observed emission. Moreover, INTEGRAL observations have shown that, while in quiescence, magnetars emit substantial persistent radiation also at higher energies, up to a few hundreds of keV. However, a convincing physical interpretation of the various spectral components is still missing.In this talk I will focus on the interpretation of magnetar spectral properties during quiescence. I will summarise the present status of the art and the currents attempts to model the broadband persistent emission of magnetars (from IR to hard Xrays) within a self consistent, physical scenario.

Sensitivity analysis for high-contrast imaging with segmented space telescopes

2018 ◽  
Author(s):  
Lucie Leboulleux ◽  
Laurent Pueyo ◽  
Jean-François Sauvage ◽  
Rémi Soummer ◽  
Thierry Fusco ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
High Contrast ◽  
Space Telescopes ◽  
Contrast Imaging ◽  
High Contrast Imaging

REMARKS ON THE GROUND STATE ENERGY OF THE SPIN-BOSON MODEL: AN APPLICATION OF THE WIGNER–WEISSKOPF MODEL

2001 ◽  
Vol 13 (02) ◽  
pp. 221-251 ◽  
Author(s):  
MASAO HIROKAWA
Keyword(s):  
Perturbation Theory ◽  
Spectral Analysis ◽  
Ground State Energy ◽  
Ground State ◽  
Spectral Properties ◽  
State Energy ◽  
Regularity Condition ◽  
Infrared Singularity ◽  
Regular Perturbation ◽  
Boson Model

For the ground state energy of the spin-boson (SB) model, we give a new upper bound in the case with infrared singularity condition (i.e. without infrared cutoff), and a new lower bound in the case of massless bosons with infrared regularity condition. We first investigate spectral properties of the Wigner–Weisskopf (WW) model, and apply them to SB model to achieve our purpose. Then, as an extra result of the spectral analysis for WW model, we show that a non-perturbative ground state appears, and its ground state energy is so low that we cannot conjecture it by using the regular perturbation theory.

scholarly journals Spectral analysis of Hahn-Dirac system

2021 ◽  
Author(s):  
Bilender Allahverdiev ◽  
Hüseyin Tuna
Keyword(s):  
Spectral Analysis ◽  
Boundary Value Problem ◽  
Spectral Properties ◽  
Orthonormal Basis ◽  
Boundary Value ◽  
Dirac System ◽  
One Dimensional ◽  
Countable Sequence ◽  
Greens Function ◽  
The One

In this paper, we study some spectral properties of the one-dimensional Hahn-Dirac boundary-value problem, such as formally self-adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Greens function, the existence of a countable sequence of eigenvalues, eigenfunctions forming an orthonormal basis of L2w,q ((w0. a): E).

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