OP: Collaborative Research: Non-Hamiltonian Wave Dynamics in Atomic & Optical Models

OP：合作研究：原子中的非哈密尔顿波动力学

• 批准号: 1602994
• 负责人: Panayotis Kevrekidis
• 金额: $ 16万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1602994&HistoricalAwards=false
• 关键词: OP; Collaborative; Research; Non; Hamiltonian

This project focusses on the effects of energy gain and/or loss when waves propagate through non-linear media. The simplest kinds of wave motion exhibit a property called isochronism which was first observed by Galileo: The frequency of oscillation of the wave is independent of its amplitude (or size). Wave media in which this simple behavior is observed are called "linear". Non-linear media are also known, in which the frequency of the wave varies with its amplitude. If the medium is also dispersive (like a prism), then waves with different frequency will travel with different speed. The combined effects of non-linearity and dispersion can be quite striking, as with the formation of solitons - stable wave patterns that propagate through the medium without changing shape. A central focus of this work is to explore how solitons and other coherent structures that form in non-linear media, such as vortices, are responsible for the localization and transport of energy and information. If the medium through which the wave propagates is dissipative, then energy is lost to friction or radiation, and so stabilizing the flow of energy and information requires energy input (gain). The work will focus especially on the interplay of gain and loss in current experimental, theoretical, and computational investigations into the behavior of non-linear media formed from ultra-cold atomic vapors. This project involves the comprehensive examination of some selected key aspects within this class of systems. The study is based on variants of one of the most prototypical and most relevant models for the evolution of nonlinear waves: the nonlinear Schroedinger (NLS) equation. The NLS equation is at the heart of a wide variety of physical phenomena including, but not limited to, optical fibers, condensed matter physics, plasma waves, and deep water freak/rogue waves in fluid mechanics. In particular, the group will study the effects of gain and loss within the realm of (A) optical systems that have the so-called Parity-Time reversal (PT) symmetry, and possess a delicate balance between external gain and intrinsic loss that can robustly sustain the existence and propagation of coherent structures, (B) finite temperature Bose-Einstein condensates which have been proposed as candidates for sustaining/processing quantum information that could potentially realize the next generation of computational architectures, and finally, (C) exciton-polariton condensates, which provide another pristine and very accessible experimental setting for the manipulation of macroscopic quantum mechanics. Within these systems, the group will explore the interplay of the intrinsic scales induced by nonlinearity and dispersion and the extrinsic ones, stemming from gain and loss, and how this interplay affects the existence, stability and dynamics of different coherent structures that are the building blocks of information storage and processing. Within this program, the group expects to generate mathematical models and methods, as well as computational techniques, that will not only shed light to these particular atomic and optical applications and their experimental observations, but which may also be of broader use for the study of other non-conservative systems.

当波通过非线性培养基传播时，该项目的重点是能量增益和/或损失的影响。最简单的波动运动表现出一种称为等级的特性，该特性首先是由伽利略观察到的：波的振荡频率与其振幅（或大小）无关。观察到这种简单行为的波介质称为“线性”。也已知非线性介质，其中波的频率随其幅度而变化。如果培养基也是分散的（例如棱镜），则频率不同的波将以不同的速度传播。非线性和色散的综合效果可能会引人注目，就像孤子的形成一样 - 稳定的波模式，它们通过培养基传播而不会变化。这项工作的一个主要重点是探索在非线性媒体中形成的孤子和其他相干结构（例如涡流）如何负责能源和信息的定位和运输。如果波传播的介质是耗散的，则能量会损失在摩擦或辐射上，因此稳定能量和信息的流动需要能量输入（增益）。这项工作将特别集中在当前实验，理论和计算调查中，对由超冷原子蒸气形成的非线性培养基的行为的相互作用。 该项目涉及对此类系统中一些选定的关键方面的全面检查。该研究基于非线性波进化的最原型和最相关模型之一的变体：非线性schroedinger（NLS）方程。 NLS方程是多种物理现象的核心，包括但不限于流体力学中的光纤，冷凝物理物理学，血浆波和深水怪胎/流氓波。特别是，该小组将研究具有所谓的平等时间逆转（PT）对称性的（a）光学系统领域内的收益和损失的影响，并在外部损失和内在损失之间具有微妙的平衡（b）有限温度Bose-Einstein凝结物的坚固存在和传播，这些凝结物被提议作为维持/加工量子信息的候选者，这些信息可能有可能实现下一代计算体系结构，最后，（c）Ickiton--偏振子冷凝物，它为操纵宏观量子力学提供了另一个原始且非常容易获得的实验设置。在这些系统中，该组将探索非线性和分散性引起的固有量表的相互作用，以及外部量表，源于增益和损失，以及该相互作用如何影响不同的相干结构的存在，稳定性和动力学，这些结构是构建块的不同相干结构信息存储和处理。 在该计划中，该小组期望生成数学模型和方法以及计算技术，这些技术不仅会阐明这些特定的原子和光学应用及其实验观察结果，而且还可以更广泛地用于研究。其他非保守系统。

项目成果

Exploring critical points of energy landscapes: From low-dimensional examples to phase field crystal PDEs

• DOI: 10.1016/j.cnsns.2020.105679
• 发表时间: 2020-08
• 期刊: Commun. Nonlinear Sci. Numer. Simul.
• 作者: P. Subramanian;I. Kevrekidis;P. Kevrekidis

Quasistable quantum vortex knots and links in anisotropic harmonically trapped Bose-Einstein condensates

各向异性谐波俘获玻色-爱因斯坦凝聚中的准稳定量子涡结和链接

• DOI: 10.1103/physreva.99.063604
• 发表时间: 2019
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Ticknor, Christopher;Ruban, Victor P.;Kevrekidis, P. G.
• 通讯作者: Kevrekidis, P. G.

Breather stripes and radial breathers of the two-dimensional sine-Gordon equation

二维正弦戈登方程的通气条纹和径向通气

• DOI: 10.1016/j.cnsns.2020.105596
• 发表时间: 2021
• 期刊: Communications in Nonlinear Science and Numerical Simulation
• 影响因子: 3.9
• 作者: Kevrekidis, P.G.;Carretero-González, R.;Cuevas-Maraver, J.;Frantzeskakis, D.J.;Caputo, J.-G.;Malomed, B.A.
• 通讯作者: Malomed, B.A.

Long-range interactions of kinks

• DOI: 10.1103/physrevd.99.016010
• 发表时间: 2018-10
• 期刊: Physical Review D
• 影响因子: 5
• 作者: I. Christov;Robert J. Decker;A. Demirkaya;V. Gani;P. Kevrekidis;R. V. Radomskiy

Decay of two-dimensional quantum turbulence in binary Bose-Einstein condensates

二元玻色-爱因斯坦凝聚中二维量子湍流的衰变

• DOI: 10.1103/physreva.103.023301
• 发表时间: 2021
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Mithun, Thudiyangal;Kasamatsu, Kenichi;Dey, Bishwajyoti;Kevrekidis, Panayotis G.
• 通讯作者: Kevrekidis, Panayotis G.