开放系统动力学的密度张量层次结构：检索 噪声

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摘要翻译：
我们为开放系统动力学引入了一个密度张量层次，它恢复了传递到约化密度矩阵中丢失的涨落信息。对于由经典概率分布引起的涨落，该层次由纯态密度矩阵元乘积的期望值形成，并可以用一个简单的母函数来紧凑地概括。对于量子系统与处于整体纯态的量子环境相互作用时产生的量子涨落，定义了相应的层次结构为全密度矩阵的系统矩阵元素乘积的环境迹。只有量子噪声等级中最低的一个成员是可以直接实验测量的。纯态密度矩阵的单位迹和幂等性质暗示了在适当的张量指数对收缩下，将n阶张量与n阶张量联系起来的张量层次的下降关系。作为说明经典概率分布形式的例子，我们考虑了一个由它随机演化的量子系统和由跳跃过程Schr-Odinger方程演化的量子系统。为说明量子涨落情形下相应的迹形式，我们考虑了无限质量布朗粒子的碰撞布朗运动和弱耦合Born-Markov主方程。后者给出了量子光学主方程和Caldeira-Leggett主方程在不同分类下的推广层次。作为密度张量的进一步应用，我们对比了约简和不约简状态向量的随机Schr Odinger方程，并讨论了耦合到量子环境中的量子系统为何表现为后者。
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英文标题：
《A density tensor hierarchy for open system dynamics: retrieving the
  noise》
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作者：
Stephen L. Adler
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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：Quantum Physics        量子物理学
分类描述：Description coming soon
描述即将到来
--
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：High Energy Physics - Phenomenology        高能物理-现象学
分类描述：Theoretical particle physics and its interrelation with experiment. Prediction of particle physics observables: models, effective field theories, calculation techniques. Particle physics: analysis of theory through experimental results.
理论粒子物理及其与实验的相互关系。粒子物理可观测物的预测：模型，有效场论，计算技术。粒子物理：通过实验结果分析理论。
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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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英文摘要：
  We introduce a density tensor hierarchy for open system dynamics, that recovers information about fluctuations lost in passing to the reduced density matrix. For the case of fluctuations arising from a classical probability distribution, the hierarchy is formed from expectations of products of pure state density matrix elements, and can be compactly summarized by a simple generating function. For the case of quantum fluctuations arising when a quantum system interacts with a quantum environment in an overall pure state, the corresponding hierarchy is defined as the environmental trace of products of system matrix elements of the full density matrix. Only the lowest member of the quantum noise hierarchy is directly experimentally measurable. The unit trace and idempotence properties of the pure state density matrix imply descent relations for the tensor hierarchies, that relate the order $n$ tensor, under contraction of appropriate pairs of tensor indices, to the order $n-1$ tensor. As examples to illustrate the classical probability distribution formalism, we consider a quantum system evolving by It\^o stochastic and by jump process Schr\"odinger equations. As examples to illustrate the corresponding trace formalism in the quantum fluctuation case, we consider collisional Brownian motion of an infinite mass Brownian particle, and the weak coupling Born-Markov master equation. In different specializations, the latter gives the hierarchies generalizing the quantum optical master equation and the Caldeira--Leggett master equation. As a further application of the density tensor, we contrast stochastic Schr\"odinger equations that reduce and that do not reduce the state vector, and discuss why a quantum system coupled to a quantum environment behaves like the latter.
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PDF链接：
https://arxiv.org/pdf/704.0796

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关键词：系统动力学 层次结构 开放系统 动力学 Mathematical 暗示 概率分布 张量 涨落 fluctuations