The Flow Equation Approach to Many-Particle Systems
The Flow Equation Approach to Many-Particle Systems
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DOI：
10.1007/3-540-34068-8
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发表时间：
2006-07
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通讯作者：
S. Kehrein
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作者：
S. Kehrein
在过去的十年里，？方程方法已发展成为量子多体物理学的一种新的理论方法。它的基本概念是由Wegner [1]和G lazek和Wilson [2，3]独立构思的：酉？这就形成了一个多粒子的哈密顿能量对角线。这个概念可以被看作是多体物理学中传统标度方法的推广，其中紫能级被降低到实验相关的低能标度[4]。主？传统的缩放方法和之间的erence？流动方程的方法，然后可以追溯到这样一个事实，即？低方程方法保留了所有的自由度，即完整的希尔伯特空间，而传统的缩放方法集中在一些低能量子空间。的一个有用功能是？因此，现在方程的方法是，它允许在一个单位的所有能量尺度上的动力学量的计算？艾德框架。自推出以来，大量的工作使用？方程方法已经积累。它被用来研究从耗散量子系统到关联电子物理的许多非常不同的量子多体问题。最近，它也变得明显，？量子多体n-平衡问题是现代理论物理的前沿问题之一，而OW方程方法是研究量子多体n-平衡问题的一种非常合适的方法。因此，时间似乎已经准备好编译的研究文献？以一种一致的、可访问的方式来运行方程，这是我写这本书的目标。
Overthepastdecade, the? owequationmethodhasdevelopedintoanewv-satile theoretical approach to quantum many-body physics. Its basic concept was conceived independently by Wegner [1] and by G lazek and Wilson [2, 3]: the derivation of a unitary? ow that makes a many-particle Hamiltonian-creasingly energy-diagonal. This concept can be seen as a generalization of theconventionalscalingapproachesinmany-bodyphysics, wheresomeult-violet energy scale is lowered down to the experimentally relevant low-energy scale [4]. The main di? erence between the conventional scaling approach and the? ow equation approach can then be traced back to the fact that the? ow equation approach retains all degrees of freedom, ie the full Hilbert space, while the conventional scaling approach focusses on some low-energy subspace. One useful feature of the? ow equation approach is therefore that it allows the calculation of dynamical quantities on all energy scales in one uni? ed framework. Since its introduction, a substantial body of work using the? ow eq-tion approach has accumulated. It was used to study a number of very d-ferent quantum many-body problems from dissipative quantum systems to correlated electron physics. Recently, it also became apparent that the? ow equation approach is very suitable for studying quantum many-body n-equilibrium problems, which form one of the current frontiers of modern theoretical physics. Therefore the time seems ready to compile the research literature on? ow equations in a consistent and accessible way, which was my goal in writing this book.