The First Century of Cosmic Rays, an Historical Overview

Jones, L. W.

doi:10.14311/ap.2013.53.0497

Cited by 2 publications

(2 citation statements)

References 4 publications

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“…Thus for a wave-packet input the enhanced reflection comes not from an increase in the overall amplitude, but instead from a lengthening of the pulse, of order L. An analogous effect was noted in the diffraction situation by Longhi [12], and the connection to the properties of error functions pointed out in Ref. [22]. …”

Section: Discussionsupporting

confidence: 53%

Analytic results for aPT-symmetric optical structure

Jones¹

2012

J. Phys. A: Math. Theor.

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Propagation of light through media with a complex refractive index in which gain and loss are engineered to be P T symmetric has many remarkable features. In particular the usual unitarity relations are not satisfied, so that the reflection coefficients can be greater than one, and in general are not the same for left or right incidence. Within the class of optical potentials of the form v(x) = v 1 cos(2βx) + iv 2 sin(2βx) the case v 2 = v 1 is of particular interest, as it lies on the boundary of P T -symmetry breaking. It has been shown in a recent paper by Lin et al. that in this case one has the property of "unidirectional invisibility", while for propagation in the other direction there is a greatly enhanced reflection coefficient proportional to L 2 , where L is the length of the medium in the direction of propagation.For this potential we show how analytic expressions can be obtained for the various transmission and reflection coefficients, which are expressed in a very succinct form in terms of modified Bessel functions. While our numerical results agree very well with those of Lin et al. we find that the invisibility is not quite exact, in amplitude or phase. As a test of our formulas we show that they identically satisfy a modified version of unitarity appropriate for P T -symmetric potentials. We also examine how the enhanced transmission comes about for a wave-packet, as opposed to a plane wave, finding that the enhancement now arises through an increase, of O(L), in the pulse length, rather than the amplitude.

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Section: Discussionsupporting

confidence: 53%

Analytic results for aPT-symmetric optical structure

Jones¹

2012

J. Phys. A: Math. Theor.

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“…While a linear scaling behavior would be expected at this point, the excited Jordan associated functions grow linearly to precisely compensate the decrease in contribution from the nondegenerate states, leading to the stalled growth. Formally, this corresponds to an incident Gaussian packet being reflected as a sum of error functions [65] and thus the incident pulse is lengthened into an extended packet of peak width ∼ L upon reflection [63].…”

Section: Pt -Symmetric Generating Potentialsmentioning

confidence: 99%

Real-time transport in open quantum systems fromPT-symmetric quantum mechanics

Elenewski

Chen

2014

Phys. Rev. B

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Nanoscale electronic transport is of intense technological interest, with applications ranging from semiconducting devices and molecular junctions to charge migration in biological systems. Most explicit theoretical approaches treat transport using a combination of density functional theory (DFT) and non-equilibrium Green's functions. This is a static formalism, with dynamic response properties accommodated only through complicated extensions. To circumvent this limitation, the carrier density may be propagated using real-time time-dependent DFT (RT-TDDFT), with boundary conditions corresponding to an open quantum system. Complex absorbing potentials can emulate outgoing particles at the simulation boundary, although these do not account for introduction of charge density. It is demonstrated that the desired positive particle flux is afforded by a class of PT -symmetric generating potentials that are characterized by anisotropic transmission resonances. These potentials add density every time a particle traverses the cell boundary, and may be used to engineer a continuous pulse train for incident packets. This is a first step toward developing a complete transport formalism unique to RT-TDDFT.

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The First Century of Cosmic Rays, an Historical Overview

Cited by 2 publications

References 4 publications

Analytic results for aPT-symmetric optical structure

Analytic results for aPT-symmetric optical structure

Real-time transport in open quantum systems fromPT-symmetric quantum mechanics

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