Heat-kernel approach for scattering

2018

Physics Letters B

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Section: Resultsmentioning

confidence: 99%

Scalar scattering in Schwarzschild spacetime: Integral equation method

Chen

2018

Physics Letters B

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“…In quantum mechanical scattering theory, the scattering amplitude is described by the scattering phase shift. We have developed a method for the calculation of the scattering phase shift based on the heat kernel theory [27,28]. This method can also be used to calculate the scattering amplitude in gravitational wave scattering.…”

Section: Resultsmentioning

confidence: 99%

Scattering theory without large-distance asymptotics

Liu

2014

J. High Energ. Phys.

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In conventional scattering theory, to obtain an explicit result, one imposes a precondition that the distance between target and observer is infinite. With the help of this precondition, one can asymptotically replace the Hankel function and the Bessel function with the sine functions so that one can achieve an explicit result. Nevertheless, after such a treatment, the information of the distance between target and observer is inevitably lost. In this paper, we show that such a precondition is not necessary: without losing any information of distance, one can still obtain an explicit result of a scattering rigorously. In other words, we give an rigorous explicit scattering result which contains the information of distance between target and observer. We show that at a finite distance, a modification factor -the Bessel polynomial -appears in the scattering amplitude, and, consequently, the cross section depends on the distance, the outgoing wave-front surface is no longer a sphere, and, besides the phase shift, there is an additional phase (the argument of the Bessel polynomial) appears in the scattering wave function.

“…The scattering phase shift is determined by solving the Helmholtz equation with the boundary condition on the obstacle. In further works, we can apply the heat-kernel method to calculate the scattering phase shift using the approach developed in [23][24][25][26].…”

Section: Discussionmentioning

confidence: 99%

Acoustic scattering theory without large-distance asymptotics

Zhou

2018

J. Phys. Commun.

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In conventional acoustic scattering theory, a large-distance asymptotic approximation is employed. In this approximation, a far-field pattern, an asymptotic approximation of the exact result, is used to describe a scattering process. The information of the distance between the target and the observer, however, is lost in the large-distance asymptotic approximation. In this paper, we provide a rigorous theory of acoustic scattering without the large-distance asymptotic approximation. The acoustic scattering treatmentdeveloped in this paper provides an improved description for the acoustic wave outside the target. Moreover, as examples, we consider acoustic scattering on a rigid sphere and on a nonrigid sphere. We also illustrate the influence of the near target effect on the angular distribution of outgoing waves. It is shown that for long wavelength acoustic scattering, the near target effect must be reckoned in.