HYDRODYNAMICS OF CORRELATED SYSTEMS
HYDRODYNAMICS OF CORRELATED SYSTEMS
复制标题
相关系统的流体动力学
DOI：
10.1007/1-4020-4531-x_5
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发表时间：
2006
影响因子：
8.6
通讯作者：
A. Abanov
中科院分区：
文献类型：
--
作者：
A. Abanov
用流体力学方法计算了量子一维多体系统基态空位形成概率的渐近性。系统的量子流体动力学被表示为流体动力学变量组态上的欧几里得路径积分。在空间大小有限的情况下，概率由瞬子构型控制，问题归结为求一类流体动力学方程的瞬子解。在建立了一般形式之后，我们对几个简单的具有任意色散的无系统费米子和Calogero-Sutherland模型进行了计算。对于这些系统，我们通过与随机矩阵理论中已知的精确结果的比较，证实了所得到的结果。我们认为，即使在线性化流体动力学失效的情况下，非线性流体动力学方法也可能是有用的。
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 con- figurations of hydrodynamic variables. In the limit of a larg e size of the empty space, the probability is dominated by an instanton configur ation, and the prob- lem is reduced to the finding of an instanton solution of class ical hydrodynamic equations. After establishing a general formalism, we carry out this calcula- tion 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.