Hydrodynamics of correlated systems. Emptiness Formation Probability and Random Matrices
Hydrodynamics of correlated systems. Emptiness Formation Probability and Random Matrices
复制标题
相关系统的流体动力学。
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
A. Abanov
中科院分区：
文献类型：
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作者：
A. Abanov
一个流体动力学的方法是用来计算的虚形成概率的渐近-在量子一维多体系统的基态形成一个空的空间的概率。系统的量子流体力学被表示为流体力学变量配置上的欧几里德路径积分。在一个大尺寸的空的空间的限制，概率是占主导地位的瞬子配置，和问题是减少到一个经典的流体动力学方程的瞬子解的发现。在建立了一般形式之后，我们对几个简单的系统--任意色散的自由费米子和Calogero-Sutherland模型进行了计算。对于这些系统，我们确认所获得的结果与随机矩阵理论中已知的精确结果进行比较。我们认为，非线性流体动力学的方法可能是有用的，即使在线性流体动力学失败的情况下。
A hydrodynamic approach is used to calculate an asymptotics of the Emptiness Formation Probability - the probability of a formation of an empty space in the ground state of a quantum one-dimensional many body system. Quantum hydrodynamics of a system is represented as a Euclidian path integral over configurations of hydrodynamic variables. In the limit of a large size of the empty space, the probability is dominated by an instanton configuration, and the problem is reduced to the finding of an instanton solution of classical hydrodynamic equations. After establishing a general formalism, we carry out this calculation for several simple systems -- free fermions with an arbitrary dispersion and Calogero-Sutherland model. For these systems we confirm the obtained results by comparison with exact results known in Random Matrix theory. We argue that the nonlinear hydrodynamic approach might be useful even in cases where the linearized hydrodynamics fails.