Continuum mechanics for quantum many-body systems: Linear response regime
Continuum mechanics for quantum many-body systems: Linear response regime
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DOI：
10.1103/physrevb.81.195106
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发表时间：
2010-01
影响因子：
3.7
通讯作者：
Xianlong Gao;Jianmin Tao;G. Vignale;I. Tokatly
中科院分区：
文献类型：
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作者：
Xianlong Gao;Jianmin Tao;G. Vignale;I. Tokatly
在假定随时间变化的波函数可以被描述为基态波函数的几何变形的前提下，我们导出了非均匀量子多体系统电流密度的封闭运动方程。通过用单个集体场描述多体系统，我们提供了一种替代传统方法的方法，传统方法强调单粒子轨道。我们把我们的方法称为量子多体系统的连续介质力学。在线性响应区，位移场的运动方程变为线性的四阶积分微分方程，其唯一输入是单粒子密度矩阵和基态的对相关函数。随着粒子数量的增加，这个方程的复杂性基本保持不变。我们证明了我们的运动方程是一个厄米本征值问题，它允许在涉及基态密度的标量积下存在一组完备的标准正交本征函数。此外，我们还证明了由该方法得到的激发能满足求和规则，从而保证了积分谱强度的准确性。我们的公式对于由单个粒子组成的系统和在高频极限下的任何多体系统都是精确的。该理论通过简单的一粒子和二粒子系统的显式计算来说明。
We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integrodifferential equation, whose only inputs are the one-particle density matrix and the pair-correlation function of the ground state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a Hermitian eigenvalue problem, which admits a complete set of orthonormal eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.