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Journal articles on the topic 'Spectral shift function'

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Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Azamov, N. A., A. L. Carey, and F. A. Sukochev. "The Spectral Shift Function and Spectral Flow." Communications in Mathematical Physics 276, no. 1 (August 28, 2007): 51–91. http://dx.doi.org/10.1007/s00220-007-0329-9.

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2

Azamov, N. A., A. L. Carey, P. G. Dodds, and F. A. Sukochev. "Operator Integrals, Spectral Shift, and Spectral Flow." Canadian Journal of Mathematics 61, no. 2 (April 1, 2009): 241–63. http://dx.doi.org/10.4153/cjm-2009-012-0.

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Abstract. We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fréchet differentiation of operator functions that sharpen existing results, and establish the Birman–Solomyak representation of the spectral shift function of M.G. Krein in terms of an average of spectral measures in the type II setting. We also exhibit a surprising connection between the spectral shift function and spectral flow.

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3

Birman, M. Sh, and A. B. Pushnitski. "Spectral shift function, amazing and multifaceted." Integral Equations and Operator Theory 30, no. 2 (June 1998): 191–99. http://dx.doi.org/10.1007/bf01238218.

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4

Potapov, Denis, Anna Skripka, and Fedor Sukochev. "Spectral shift function of higher order." Inventiones mathematicae 193, no. 3 (November 17, 2012): 501–38. http://dx.doi.org/10.1007/s00222-012-0431-2.

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5

GEISLER, R., V. KOSTRYKIN, and R. SCHRADER. "CONCAVITY PROPERTIES OF KREIN’S SPECTRAL SHIFT FUNCTION." Reviews in Mathematical Physics 07, no. 02 (February 1995): 161–81. http://dx.doi.org/10.1142/s0129055x95000098.

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We prove that the integrated Krein’s spectral shift function for one particle Schrödinger operators in R3 is concave with respect to the perturbation potential. The proof is given by showing that the spectral shift function is the limit in the distributional sense of the difference of the counting functions for the given Hamiltonian and the free Hamiltonian in a finite domain Λ with Dirichlet boundary conditions when Λ→∞.

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6

Man Lo, Pok. "Phase shift and spectral function from PWA." EPJ Web of Conferences 199 (2019): 05024. http://dx.doi.org/10.1051/epjconf/201919905024.

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I illustrate a robust method for extracting an effective phase shift and an effective spectral weight for a coupled-channel system. These quantities are useful for describing the thermodynamics of an interacting hadron gas within the S-matrix formulation.

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7

Bruneau, Vincent, and Mouez Dimassi. "Weak asymptotics of the spectral shift function." Mathematische Nachrichten 280, no. 11 (August 2007): 1230–43. http://dx.doi.org/10.1002/mana.200410549.

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8

Albeverio, Sergio, Konstantin A. Makarov, and Alexander K. Motovilov. "Graph Subspaces and the Spectral Shift Function." Canadian Journal of Mathematics 55, no. 3 (June 1, 2003): 449–503. http://dx.doi.org/10.4153/cjm-2003-020-7.

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AbstractWe obtain a new representation for the solution to the operator Sylvester equation in the form of a Stieltjes operator integral. We also formulate new sufficient conditions for the strong solvability of the operator Riccati equation that ensures the existence of reducing graph subspaces for block operator matrices. Next, we extend the concept of the Lifshits-Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Based on this new concept we express the spectral shift function arising in a perturbation problem for block operator matrices in terms of the angular operators associated with the corresponding perturbed and unperturbed eigenspaces.

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9

Petkov, Vesselin, and Vincent Bruneau. "Meromorphic continuation of the spectral shift function." Duke Mathematical Journal 116, no. 3 (March 2003): 389–430. http://dx.doi.org/10.1215/s0012-7094-03-11631-2.

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10

Rzeszotnik, Ziemowit, and Marcin Bownik. "The spectral function of shift-invariant spaces." Michigan Mathematical Journal 51, no. 2 (April 2003): 387–414. http://dx.doi.org/10.1307/mmj/1060013204.

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11

Boyadzhiev, Khristo N. "Kreĭn's trace formula and the spectral shift function." International Journal of Mathematics and Mathematical Sciences 25, no. 4 (2001): 239–52. http://dx.doi.org/10.1155/s0161171201004318.

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LetA,Bbe two selfadjoint operators whose differenceB−Ais trace class. Kreĭn proved the existence of a certain functionξ∈L1(ℝ)such thattr[f(B)−f(A)]=∫ℝf′(x)ξ(x)dxfor a large set of functionsf. We give here a new proof of this result and discuss the class of admissible functions. Our proof is based on the integral representation of harmonic functions on the upper half plane and also uses the Baker-Campbell-Hausdorff formula.

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12

Sweeney, Daniel C., Dennis M. Sweeney, and Christian M. Petrie. "Graphical Optimization of Spectral Shift Reconstructions for Optical Backscatter Reflectometry." Sensors 21, no. 18 (September 14, 2021): 6154. http://dx.doi.org/10.3390/s21186154.

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Optical backscatter reflectometry (OBR) is an interferometric technique that can be used to measure local changes in temperature and mechanical strain based on spectral analyses of backscattered light from a singlemode optical fiber. The technique uses Fourier analyses to resolve spectra resulting from reflections occurring over a discrete region along the fiber. These spectra are cross-correlated with reference spectra to calculate the relative spectral shifts between measurements. The maximum of the cross-correlated spectra—termed quality—is a metric that quantifies the degree of correlation between the two measurements. Recently, this quality metric was incorporated into an adaptive algorithm to (1) selectively vary the reference measurement until the quality exceeds a predefined threshold and (2) calculate incremental spectral shifts that can be summed to determine the spectral shift relative to the initial reference. Using a graphical (network) framework, this effort demonstrated the optimal reconstruction of distributed OBR measurements for all sensing locations using a maximum spanning tree (MST). By allowing the reference to vary as a function of both time and sensing location, the MST and other adaptive algorithms could resolve spectral shifts at some locations, even if others can no longer be resolved.

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13

Pushnitski, Alexander. "The Spectral Shift Function and the Invariance Principle." Journal of Functional Analysis 183, no. 2 (July 2001): 269–320. http://dx.doi.org/10.1006/jfan.2001.3751.

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14

Azamov, Nurulla, and Tom Daniels. "Singular spectral shift function for resolvent comparable operators." Mathematische Nachrichten 292, no. 9 (June 6, 2019): 1911–30. http://dx.doi.org/10.1002/mana.201700293.

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15

Potapov, Denis, and Fedor Sukochev. "Koplienko Spectral Shift Function on the Unit Circle." Communications in Mathematical Physics 309, no. 3 (September 20, 2011): 693–702. http://dx.doi.org/10.1007/s00220-011-1338-2.

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16

Bruneau, Vincent, and Vesselin Petkov. "REPRESENTATION OF THE SPECTRAL SHIFT FUNCTION AND SPECTRAL ASYMPTOTICS FOR TRAPPING PERTURBATIONS." Communications in Partial Differential Equations 26, no. 11-12 (November 1, 2001): 2081–119. http://dx.doi.org/10.1081/pde-100107816.

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17

Pliev, M., F. Sukochev, and D. Zanin. "$$L_p-$$Bounds for the Krein Spectral Shift Function: $$0." Russian Journal of Mathematical Physics 27, no. 4 (October 2020): 491–99. http://dx.doi.org/10.1134/s1061920820040093.

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18

Bony, Jean-François, Vincent Bruneau, and Georgi Raikov. "Resonances and Spectral Shift Function near the Landau levels." Annales de l’institut Fourier 57, no. 2 (2007): 629–71. http://dx.doi.org/10.5802/aif.2270.

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19

Kostrykin, Vadim. "Concavity of Eigenvalue Sums and the Spectral Shift Function." Journal of Functional Analysis 176, no. 1 (September 2000): 100–114. http://dx.doi.org/10.1006/jfan.2000.3620.

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20

Safronov, O. "Spectral Shift Function in the Large Coupling Constant Limit." Journal of Functional Analysis 182, no. 1 (May 2001): 151–69. http://dx.doi.org/10.1006/jfan.2000.3720.

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21

Bruneau, Vincent, and Georgi D. Raikov. "High energy asymptotics of the magnetic spectral shift function." Journal of Mathematical Physics 45, no. 9 (September 2004): 3453–61. http://dx.doi.org/10.1063/1.1776643.

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22

Kohmoto, Mahito, Tohru Koma, and Shu Nakamura. "The Spectral Shift Function and the Friedel Sum Rule." Annales Henri Poincaré 14, no. 5 (November 16, 2012): 1413–24. http://dx.doi.org/10.1007/s00023-012-0219-3.

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23

Dimassi, Mouez. "Spectral Shift Function in the Large Coupling Constant Limit." Annales Henri Poincaré 7, no. 3 (April 18, 2006): 513–25. http://dx.doi.org/10.1007/s00023-005-0258-0.

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24

Adamjan, Vadim, and Heinz Langer. "The Spectral Shift Function for Certain Block Operator Matrices." Mathematische Nachrichten 211, no. 1 (March 2000): 5–24. http://dx.doi.org/10.1002/(sici)1522-2616(200003)211:1<5::aid-mana5>3.0.co;2-u.

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25

Sarason, Donald. "Book Review: Treatise on the shift operator. Spectral function theory." Bulletin of the American Mathematical Society 16, no. 2 (April 1, 1987): 297–99. http://dx.doi.org/10.1090/s0273-0979-1987-15522-4.

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26

Pushnitski, Alexander. "Estimates for the spectral shift function of the polyharmonic operator." Journal of Mathematical Physics 40, no. 11 (November 1999): 5578–92. http://dx.doi.org/10.1063/1.533047.

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27

Khochman, Abdallah. "Resonances and spectral shift function for a magnetic Schrödinger operator." Journal of Mathematical Physics 50, no. 4 (April 2009): 043507. http://dx.doi.org/10.1063/1.3087429.

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28

Koplienko, L. S. "Local conditions for the existence of the spectral shift function." Journal of Soviet Mathematics 34, no. 6 (September 1986): 2080–90. http://dx.doi.org/10.1007/bf01741582.

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29

Azamov, N. A., P. G. Dodds, and F. A. Sukochev. "The Krein Spectral Shift Function in Semifinite von Neumann Algebras." Integral Equations and Operator Theory 55, no. 3 (June 3, 2006): 347–62. http://dx.doi.org/10.1007/s00020-006-1441-5.

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30

Nakamura, Shu. "Spectral Shift Function for Trapping Energies¶in the Semiclassical Limit." Communications in Mathematical Physics 208, no. 1 (December 1, 1999): 173–93. http://dx.doi.org/10.1007/s002200050753.

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31

Hundertmark, Dirk, and Barry Simon. "An optimalL p -bound on the Krein spectral shift function." Journal d'Analyse Mathématique 87, no. 1 (December 2002): 199–208. http://dx.doi.org/10.1007/bf02868474.

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32

Lampel, Johannes, Yang Wang, Andreas Hilboll, Steffen Beirle, Holger Sihler, Janis Puķīte, Ulrich Platt, and Thomas Wagner. "The tilt effect in DOAS observations." Atmospheric Measurement Techniques 10, no. 12 (December 12, 2017): 4819–31. http://dx.doi.org/10.5194/amt-10-4819-2017.

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Abstract. Experience of differential atmospheric absorption spectroscopy (DOAS) shows that a spectral shift between measurement spectra and reference spectra is frequently required in order to achieve optimal fit results, while the straightforward calculation of the optical density proves inferior. The shift is often attributed to temporal instabilities of the instrument but implicitly solved the problem of the tilt effect discussed/explained in this paper. Spectral positions of Fraunhofer and molecular absorption lines are systematically shifted for different measurement geometries due to an overall slope – or tilt – of the intensity spectrum. The phenomenon has become known as the tilt effect for limb satellite observations, where it is corrected for in a first-order approximation, whereas the remaining community is less aware of its cause and consequences. It is caused by the measurement process, because atmospheric absorption and convolution in the spectrometer do not commute. Highly resolved spectral structures in the spectrum will first be modified by absorption and scattering processes in the atmosphere before they are recorded with a spectrometer, which convolves them with a specific instrument function. In the DOAS spectral evaluation process, however, the polynomial (or other function used for this purpose) accounting for broadband absorption is applied after the convolution is performed. In this paper, we derive that changing the order of the two modifications of the spectra leads to different results. Assuming typical geometries for the observations of scattered sunlight and a spectral resolution of 0.6 nm, this effect can be interpreted as a spectral shift of up to 1.5 pm, which is confirmed in the actual analysis of the ground-based measurements of scattered sunlight as well as in numerical radiative transfer simulations. If no spectral shift is allowed by the fitting routine, residual structures of up to 2.5 × 10−3 peak-to-peak are observed. Thus, this effect needs to be considered for DOAS applications aiming at an rms of the residual of 10−3 and below.

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33

KHOCHMAN, ABDALLAH. "RESONANCES AND SPECTRAL SHIFT FUNCTION FOR THE SEMI-CLASSICAL DIRAC OPERATOR." Reviews in Mathematical Physics 19, no. 10 (November 2007): 1071–115. http://dx.doi.org/10.1142/s0129055x0700319x.

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We consider the selfadjoint operator H = H0+ V, where H0is the free semi-classical Dirac operator on ℝ3. We suppose that the smooth matrix-valued potential V = O(〈x〉-δ), δ > 0, has an analytic continuation in a complex sector outside a compact. We define the resonances as the eigenvalues of the non-selfadjoint operator obtained from the Dirac operator H by complex distortions of ℝ3. We establish an upper bound O(h-3) for the number of resonances in any compact domain. For δ > 3, a representation of the derivative of the spectral shift function ξ(λ,h) related to the semi-classical resonances of H and a local trace formula are obtained. In particular, if V is an electro-magnetic potential, we deduce a Weyl-type asymptotics of the spectral shift function. As a by-product, we obtain an upper bound O(h-2) for the number of resonances close to non-critical energy levels in domains of width h and a Breit–Wigner approximation formula for the derivative of the spectral shift function.

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34

Bello, Valentina, Alberto Simoni, and Sabina Merlo. "Spectral Phase Shift Interferometry for Refractive Index Monitoring in Micro-Capillaries." Sensors 20, no. 4 (February 14, 2020): 1043. http://dx.doi.org/10.3390/s20041043.

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In this work, we demonstrate spectral phase-shift interferometry operating in the near-infrared wavelength range for refractive index (RI) monitoring of fluidic samples in micro-capillaries. A detailed theoretical model was developed to calculate the phase-sensitive spectral reflectivity when low-cost rectangular glass micro-capillaries, filled with samples with different refractive indices, are placed at the end of the measurment arm of a Michelson interferometer. From the phase-sensitive spectral reflectivity, we recovered the cosine-shaped interferometric signal as a function of the wavelength, as well as its dependence on the sample RI. Using the readout radiation provided by a 40-nm wideband light source with a flat emission spectrum centered at 1.55 µm and a 2 × 1 fiberoptic coupler on the common input-output optical path, experimental results were found to be in good agreement with the expected theoretical behavior. The shift of the micro-capillary optical resonances, induced by RI variations in the filling fluids (comparing saline solution with respect to distilled water, and isopropanol with respect to ethanol) were clearly detected by monitoring the positions of steep phase jumps in the cosine-shaped interferometric signal recorded as a function of the wavelength. By adding a few optical components to the instrumental configuration previously demonstrated for the spectral amplitude detection of resonances, we achieved phase-sensitive detection of the wavelength positions of the resonances as a function of the filling fluid RI. The main advantage consists of recovering RI variations by detecting the wavelength shift of “sharp peaks”, with any amplitude above a threshold in the interferometric signal derivative, instead of “wide minima” in the reflected power spectra, which are more easily affected by uncertainties due to amplitude fluctuations.

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35

Azamov, Nurulla, and Tom Daniels. "Resonance index and singular μ-invariant." Analysis 40, no. 3 (August 1, 2020): 151–61. http://dx.doi.org/10.1515/anly-2019-0053.

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AbstractGiven a self-adjoint operator and a relatively trace class perturbation, one can associate the singular spectral shift function – an integer-valued function on the real line which measures the flow of singular spectrum, not only at points outside of the essential spectrum, where it coincides with the classical notion of spectral flow, but at points within the essential spectrum too. The singular spectral shift function coincides with both the total resonance index and the singular μ-invariant. In this paper we give a direct proof of the equality of the total resonance index and singular μ-invariant assuming only the limiting absorption principle and no condition of trace class type – a context in which the existence of the singular spectral shift function is an open question. The proof is based on an application of the argument principle to the poles and zeros of the analytic continuation of the scattering matrix considered as a function of the coupling parameter.

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36

Rybkin, A. V. "THE SPECTRAL SHIFT FUNCTION, THE CHARACTERISTIC FUNCTION OF A CONTRACTION, AND A GENERALIZED INTEGRAL." Russian Academy of Sciences. Sbornik Mathematics 83, no. 1 (February 28, 1995): 237–81. http://dx.doi.org/10.1070/sm1995v083n01abeh003589.

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37

Dimassi, Mouez, and Maher Zerzeri. "Spectral shift function for slowly varying perturbation of periodic Schrödinger operators." Cubo (Temuco) 14, no. 1 (2012): 29–47. http://dx.doi.org/10.4067/s0719-06462012000100004.

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38

McGillivray, I. "The spectral shift function for planar obstacle scattering at low energy." Mathematische Nachrichten 286, no. 11-12 (March 21, 2013): 1208–39. http://dx.doi.org/10.1002/mana.201100317.

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39

DIMASSI, MOUEZ, and VESSELIN PETKOV. "SPECTRAL SHIFT FUNCTION FOR OPERATORS WITH CROSSED MAGNETIC AND ELECTRIC FIELDS." Reviews in Mathematical Physics 22, no. 04 (May 2010): 355–80. http://dx.doi.org/10.1142/s0129055x10003941.

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We obtain a representation formula for the derivative of the spectral shift function ξ(λ; B, ∊) related to the operators [Formula: see text] and H(B, ∊) = H0(B, ∊) + V(x, y), B > 0, ∊ > 0. We establish a limiting absorption principle for H(B, ∊) and an estimate [Formula: see text] for ξ′(λ; B, ∊), provided λ ∉ σ(Q), where [Formula: see text].

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40

Demirel, Semra. "The spectral shift function and Levinson's theorem for quantum star graphs." Journal of Mathematical Physics 53, no. 8 (August 2012): 082110. http://dx.doi.org/10.1063/1.4746158.

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41

Borovyk, Vita, and Konstantin A. Makarov. "On the Weak and Ergodic Limit of the Spectral Shift Function." Letters in Mathematical Physics 100, no. 1 (September 3, 2011): 1–15. http://dx.doi.org/10.1007/s11005-011-0524-7.

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42

Dimassi, Mouez, and Maher Zerzeri. "A time-independent approach for the study of spectral shift function." Comptes Rendus Mathematique 350, no. 7-8 (April 2012): 375–78. http://dx.doi.org/10.1016/j.crma.2012.03.016.

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43

Mohapatra, A., and Kakyan B. Sinha. "Spectral shift function and trace formula for unitaries?A new proof." Integral Equations and Operator Theory 24, no. 3 (September 1996): 285–97. http://dx.doi.org/10.1007/bf01204602.

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44

Hundertmark, Dirk, Rowan Killip, Shu Nakamura, Peter Stollmann, and Ivan Veselić. "Bounds on the Spectral Shift Function and the Density of States." Communications in Mathematical Physics 262, no. 2 (December 9, 2005): 489–503. http://dx.doi.org/10.1007/s00220-005-1460-0.

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45

Gesztesy, Fritz, and Konstantin A. Makarov. "The Ξ operator and its relation to Krein's spectral shift function." Journal d'Analyse Mathématique 81, no. 1 (December 2000): 139–83. http://dx.doi.org/10.1007/bf02788988.

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46

KOSTRYKIN, VADIM, and ROBERT SCHRADER. "THE DENSITY OF STATES AND THE SPECTRAL SHIFT DENSITY OF RANDOM SCHRÖDINGER OPERATORS." Reviews in Mathematical Physics 12, no. 06 (June 2000): 807–47. http://dx.doi.org/10.1142/s0129055x00000320.

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In this article we continue our analysis of Schrödinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift function per unit interaction volume. This density equals the difference of the density of states for the free and the interaction theory. This extends the results previously obtained by the authors in one dimension. Also we consider the case where the interaction is concentrated near a hyperplane.

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47

Zhao, L. B., and F. L. Liu. "Balmer-series spectral lines for hydrogen atoms in parallel magnetic and electric fields of white dwarfs." Monthly Notices of the Royal Astronomical Society 507, no. 2 (August 5, 2021): 2283–99. http://dx.doi.org/10.1093/mnras/stab2254.

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ABSTRACT We extended the two-dimensional B-spline approach recently developed to investigate the influence of a strong electric field on atomic structures and spectra for hydrogen atoms in magnetic fields of white dwarfs. Spectral lines for hydrogen in parallel magnetic and electric fields have been calculated. Wavelengths and oscillator strengths are presented for 14 Balmer α transitions as a function of magnetic and electric fields. The magnetic and electric field strengths involved span a scope, respectively, from around 23.5 to 2350 MG, and from 0 to 108 V/m. Our calculations show that the shift of Balmer-series spectral lines induced by a strong electric field reduces as the magnetic field strength increases. The obtained energy levels, wavelengths, and oscillator strengths are compared to available results in the literature, and excellent agreement was discovered. The spectral data reported in this paper can be applied to interpret the shifts of spectral lines of hydrogen in magnetic white dwarfs due to the presence of electric fields, and to predict additional spectral lines dipole-forbidden in a pure magnetic field.

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48

Albakri, Mohammad I., and Pablo A. Tarazaga. "Electromechanical impedance–based damage characterization using spectral element method." Journal of Intelligent Material Systems and Structures 28, no. 1 (July 28, 2016): 63–77. http://dx.doi.org/10.1177/1045389x16642534.

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The high-frequency nature of impedance-based structural health monitoring makes the utilization of impedance signature for model-based damage characterization a challenging problem. In this study, a novel damage characterization approach that utilizes impedance signature measured with a single piezoelectric wafer is developed. Length-varying spectral elements are introduced to minimize the total number of elements required to describe the system, along with the number of damage characterization parameters. Several objective function definitions are studied and their behaviour with respect to each damage parameter is investigated. It has been found that an objective function definition based on the frequency shift in impedance peaks is the most effective definition compared to root mean square deviation and correlation-based objective functions. A novel damage localization method, referred to as sine-fit localization method, is developed based on the underlying periodic behaviour of impedance peak shifts as a function of damage location. The sine-fit localization method is integrated with gradient descend method in a two-stage optimization algorithm for damage characterization. The developed algorithm is capable of solving the ill-posed problem of damage characterization with few iterations and small number of objective function evaluations, which makes it computationally very efficient.

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49

Dimassi, Mouez, and Vesselin Petkov. "Spectral shift function and resonances for non-semi-bounded and Stark Hamiltonians." Journal de Mathématiques Pures et Appliquées 82, no. 10 (October 2003): 1303–42. http://dx.doi.org/10.1016/s0021-7824(03)00062-x.

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50

Kukulin, V. I., V. N. Pomerantsev, and O. A. Rubtsova. "Discrete representation of the spectral shift function and the multichannel S-matrix." JETP Letters 90, no. 5 (November 2009): 402–6. http://dx.doi.org/10.1134/s0021364009170184.

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