Linear and nonlinear Bragg diffraction by electromagnetically induced gratings with 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>
 symmetry and their active control in a Rydberg atomic gas

Gao, Jie; Hang, Chao; Huang, Guoxiang

doi:10.1103/physreva.105.063511

Cited by 10 publications

(1 citation statement)

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“…In recent years, unconventional optical modulation has been introduced into the EIG structure to explore novel diffraction modes or new modulation methods. Based on increasingly attractive optical parity-time symmetric (PT ) [42][43][44][45][46] and parity-time antisymmetric (APT ) optical systems [47][48][49], asymmetric optical diffraction gratings provide a new diffraction mode [50][51][52][53][54][55]. It is notable to achieve perfect positive or negative angle diffraction in symmetric structures.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Difficulty Levels of Examples in High School Mathematics Textbooks

Jiang

Wang

2021

School Mathematics Textbooks in China

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In this paper, we address exponential ergodicity for Lévy driven Langevin dynamics with singular potentials, which can be used to model the time evolution of a molecular system consisting of N particles moving in R d and subject to discontinuous stochastic forces. In particular, our results are applicable to the singular setups concerned with not only the Lennard-Jones-like interaction potentials but also the Coulomb potentials. In addition to Harris' theorem, the approach is based on novel constructions of proper Lyapunov functions (which are completely different from the setting for Langevin dynamics driven by Brownian motions), on invoking the Hörmander theorem for non-local operators and on solving the issue on an approximate controllability of the associated deterministic system as well as on exploiting the time-change idea.

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