Scattering theory without large-distance asymptotics in arbitrary dimensions

Li, Wen-Du; Dai, Wu-Sheng

doi:10.1088/1751-8113/49/46/465202

Cited by 22 publications

(23 citation statements)

References 50 publications

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“…As a result, information about the angular current contributions [25], and the distance between target and observer is lost in this analysis. In reports by Dai et al, [26,27] it has been shown that a rigorous scattering treatment without the asymptotic approximations introduces a modification factor to the scattering amplitude, and an additional phase factor to the scattered wavefunction. Hence, our first aim is to formulate a framework to obtain the scattering properties without applying asymptotic BCs.…”

Section: Planewave Sourcementioning

confidence: 99%

Scalable first-principles-informed quantum transport theory in two-dimensional materials

Bharadwaj,

Ramasubramaniam,

Ram-Mohan

2020

Preprint

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Accurate determination of carrier transport properties in two-dimensional (2D) materials is critical for designing high-performance nano-electronic devices and quantum information platforms. While first-principles calculations effectively determine the atomistic potentials associated with defects and impurities, they are ineffective for direct modeling of carrier transport properties at length scales relevant for device applications. Here, we develop a scalable first-principles-informed quantum transport theory to investigate the carrier transport properties of 2D materials. We derive a nonasymptotic quantum scattering framework to obtain transport properties in proximity to scattering centers. We then bridge our scattering framework with k • p perturbation theory, with inputs from first-principles electronic structure calculations, to construct a versatile multiscale formalism that enables modeling of realistic devices at the mesoscale. Our formalism also accounts for the crucial contributions of decaying evanescent modes across heterointerfaces. We apply this formalism to study electron transport in lateral transition-metal dichalcogenide (TMDC) heterostructures and show that material inclusions can lead to an enhancement in electron mobility by an order of magnitude larger than pristine TMDCs.

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Section: Planewave Sourcementioning

confidence: 99%

Scalable first-principles-informed quantum transport theory in two-dimensional materials

Bharadwaj,

Ramasubramaniam,

Ram-Mohan

2020

Preprint

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“…(5.15) still diverges. However, the divergence can be removed by a renormalization procedure [12]. We will illustrate such a renormalization procedure by taking the Cauchy distribution as an example in section 6.2.5.…”

Section: Probability One-loop Effective Actionmentioning

confidence: 99%

Probability Thermodynamics and Probability Quantum Field

Zhang,

Li,

Liu

et al. 2019

Preprint

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In this paper, we introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a certain statistical distribution. Eigenvalue spectra define spectral functions. Various thermodynamic quantities in thermodynamics and effective actions in quantum field theory are all spectral functions. In the scheme, eigenvalues obey a probability distribution, so a probability distribution determines a family of spectral functions in thermodynamics and in quantum field theory. This leads to probability thermodynamics and probability quantum fields determined by a probability distribution. There are two types of spectra: lower bounded spectra, corresponding to the probability distribution with nonnegative random variables, and the lower unbounded spectra, corresponding to probability distributions with negative random variables. For lower unbounded spectra, we use the generalized definition of spectral functions. In some cases, we encounter divergences. We remove the divergence by a renormalization procedure. Moreover, in virtue of spectral theory in physics, we generalize some concepts in probability theory. For example, the moment generating function in probability theory does not always exist. We redefine the moment generating function as the generalized heat kernel, which makes the concept definable when the definition in probability theory fails. As examples, we construct examples corresponding to some probability distributions. Thermodynamic quantities, vacuum amplitudes, one-loop effective actions, and vacuum energies for various probability distributions are presented.

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“…The phase shift δ l . For scattering of a plane wave by a spherically symmetric target, the solution of equation (1.1) can be written as a linear combination of the spherical Hankel function [3,6]…”

Section: Scattering Phase Shiftmentioning

confidence: 99%

“…Recently, a rigorous scattering theory without large-distance asymptotics in quantum mechanics is developed [5,6]. In this scattering theory, the information of the distance between the target and the observer is taken into account, since there is no large-distance asymptotic approximation.…”

Section: Introductionmentioning

confidence: 99%

Acoustic scattering theory without large-distance asymptotics

Zhou

Dai

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.

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Scattering theory without large-distance asymptotics in arbitrary dimensions

Cited by 22 publications

References 50 publications

Scalable first-principles-informed quantum transport theory in two-dimensional materials

Scalable first-principles-informed quantum transport theory in two-dimensional materials

Probability Thermodynamics and Probability Quantum Field

Acoustic scattering theory without large-distance asymptotics

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