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Books on the topic 'Scattering matrix method'

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Author: Grafiati

Published: 14 March 2023

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1

Thomas, Wriedt, and Eremin Yuri, eds. Light scattering by systems of particles: Null-field method with discrete sources : theory and programs. Berlin: Springer, 2006.

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2

C, Hill S., ed. Light scattering by particles: Computational methods. Singapore: World Scientific, 1990.

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3

G, Burke P., and Berrington Keith A, eds. Atomic and molecular processes: An R-matrix approach. Bristol: Institute of Physics Pub., 1993.

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4

Chain-scattering approach to h[infinity] control. Boston: Birkhauser, 2012.

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5

Abdelmonem, Mohamed S., Eric J. Heller, Abdulaziz D. Alhaidari, and Hashim A. Yamani. J-Matrix Method: Developments and Applications. Springer Netherlands, 2010.

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6

The J-matrix method: Developments and applications. Dordrecht: Springer, 2008.

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7

(Editor), Abdulaziz D. Alhaidari, Eric J. Heller (Editor), H. A. Yamani (Editor), and Mohamed S. Abdelmonem (Editor), eds. The J-matrix Method: Recent Developments and Selected Applications. Springer, 2008.

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8

Kachelriess, Michael. Scattering processes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0009.

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The unitarity of the S-matrix is used to derive the optical theorem. The connection between Green functions and scattering amplitudes given by the LSZ reduction formula is derived. The trace and the helicity method are developed and applied to the calculation of QED processes. The emission of soft photons and gravitons is discussed. In an appendix, the connection between S-matrix elements, Feynman amplitudes and decay rates or cross-sections is derived.

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9

Invariant Imbedding T-Matrix Method for Light Scattering by Nonspherical and Inhomogeneous Particles. Elsevier, 2020. http://dx.doi.org/10.1016/c2018-0-02999-0.

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10

Yang, Ping, Michael Kahnert, Bingqiang Sun, Lei Bi, and George Kattawar. Invariant Imbedding T-Matrix Method for Light Scattering by Nonspherical and Inhomogeneous Particles. Elsevier, 2019.

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11

Yang, Ping, Michael Kahnert, Bingqiang Sun, Lei Bi, and George Kattawar. Invariant Imbedding T-Matrix Method for Light Scattering by Nonspherical and Inhomogeneous Particles. Elsevier, 2019.

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12

Boudreau, Joseph F., and Eric S. Swanson. Quantum mechanics I–few body systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0021.

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Several techniques for obtaining the eigenspectrum and scattering properties of one- and two-body quantum systems are presented. More unusual topics, such as solving the Schrödinger equation in momentum space or implementing relativistic kinematics, are also addressed. A novel quantum Monte Carlo technique that leverages the similarity between path integrals and random walks is developed. An exploration of the method for simple problems is followed by a survey of methods to obtain ground state matrix elements. A review of scattering theory follows. The momentum space T-matrix formalism for scattering is introduced and an efficient numerical method for solving the relevant equations is presented. Finally, the method is extended to the coupled channel scattering problem.

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13

Horing, Norman J. Morgenstern. Retarded Green’s Functions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0005.

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Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, which represent the time development of one (or a few) state(s) that may be understood as localized but are in interaction with a continuum of states, are discussed and applied to chemisorption. Introductions are also made to the Dyson integral equation, T-matrix and the Dirac delta-function potential, with the latter applied to random impurity scattering. The retarded Green’s function in the presence of random impurity scattering is exhibited in the Born and self-consistent Born approximations, with application to Ando’s semi-elliptic density of states for the 2D Landau-quantized electron-impurity system. Important retarded Green’s functions and their methods of derivation are discussed. These include Green’s functions for electrons in magnetic fields in both three dimensions and two dimensions, also a Hamilton equation-of-motion method for the determination of Green’s functions with application to a 2D saddle potential in a time-dependent electric field. Moreover, separable Hamiltonians and their product Green’s functions are discussed with application to a one-dimensional superlattice in axial electric and magnetic fields. Green’s function matching/joining techniques are introduced and applied to spatially varying mass (heterostructures) and non-local electrostatics (surface plasmons).

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14

Muller, Sebastian, and Martin Sieber. Resonance scattering of waves in chaotic systems. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.34.

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This article discusses some applications of random matrix theory (RMT) to quantum or wave chaotic resonance scattering. It first provides an overview of selected topics on universal statistics of resonances and scattering observables, with emphasis on theoretical results obtained via non-perturbative methods starting from the mid-1990s. It then considers the statistical properties of scattering observables at a given fixed value of the scattering energy, taking into account the maximum entropy approach as well as quantum transport and the Selberg integral. It also examines the correlation properties of the S-matrix at different values of energy and concludes by describing other characteristics and applications of RMT to resonance scattering of waves in chaotic systems, including those relating to time delays, quantum maps and sub-unitary random matrices, and microwave cavities at finite absorption.

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15

Mathematical Theory of Scattering Resonances. American Mathematical Society, 2019.

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