摘要翻译：
我们提出了一系列的方法，解析的和数值的，可以描述（非）平衡系综中的行为，包括经典的和量子的，特别是在复杂系统中，标准方法不能应用。我们证明了从Wigner-von Neumann-Moyal-Lindblad方程量子体系中产生的各种集体模型中的基本定域模产生非平凡的（元）稳定态（模式），定域的、混沌的、纠缠的或退相干的，它们是经典BBGKY体系的“Wignerization”过程的结果，是由Wigner-von Neumann-Moyal-Lindblad方程的量子体系中的“Wignerization”过程产生的。我们通过精确的解析/数值计算给出了内量子动力学的显式描述。
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英文标题：
《Pattern Formation in Quantum Ensembles》
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作者：
Antonina N. Fedorova, Michael G. Zeitlin
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Quantum Physics        量子物理学
分类描述：Description coming soon
描述即将到来
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Physics        物理学
二级分类：Pattern Formation and Solitons        图形形成与孤子
分类描述：Pattern formation, coherent structures, solitons
图案形成，相干结构，孤子
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一级分类：Physics        物理学
二级分类：Plasma Physics        等离子体物理学
分类描述：Fundamental plasma physics. Magnetically Confined Plasmas (includes magnetic fusion energy research). High Energy Density Plasmas (inertial confinement plasmas, laser-plasma interactions). Ionospheric, Heliophysical, and Astrophysical plasmas (includes sun and solar system plasmas). Lasers, Accelerators, and Radiation Generation. Low temperature plasmas and plasma applications (include dusty plasmas, semiconductor etching, plasma-based nanotechnology, medical applications). Plasma Diagnostics, Engineering and Enabling Technologies (includes fusion reactor design, heating systems, diagnostics, experimental techniques)
基础等离子体物理。磁约束等离子体（包括磁聚变能研究）。高能量密度等离子体（惯性约束等离子体，激光-等离子体相互作用）。电离层、太阳物理和天体物理等离子体（包括太阳和太阳系等离子体）。激光，加速器和辐射产生。低温等离子体和等离子体应用（包括尘埃等离子体、半导体蚀刻、基于等离子体的纳米技术、医疗应用）。等离子体诊断、工程和使能技术（包括聚变反应堆设计、加热系统、诊断、实验技术）
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英文摘要：
  We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from basic localized modes in various collective models arising from the quantum hierarchy of Wigner-von Neumann-Moyal-Lindblad equations, which are the result of ``wignerization'' procedure of classical BBGKY hierarchy. We present the explicit description of internal quantum dynamics by means of exact analytical/numerical computations.
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PDF链接：
https://arxiv.org/pdf/711.0724