论文标题
通过扰动表现出带矩阵结构的量子多体松弛的修饰
Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure
论文作者
论文摘要
我们研究了如何根据非驱动性典型性框架内的弱到中度扰动来修改孤立量子多体系统的可观察到的放松行为。所谓的扰动曲线扮演着一个关键角色，这表征了扰动矩阵元素在未受扰动的哈密顿元素对相应能量特征值差的差异中的依赖性依赖性。特别是，带有带的矩阵结构是通过扰动曲线定量捕获的，该轮廓接近零能量差异。松弛的时间修改通过非线性积分方程与扰动曲线有关，该方程允许近似分析解决方案，以实现足够弱且强烈的扰动，并在一般情况下我们制定了数值解决方案。例如，我们考虑一个具有明显带状矩阵结构的自旋晶格模型，并且我们发现数字与我们的分析预测相当一致，而没有任何自由拟合参数。
We investigate how the observable relaxation behavior of an isolated quantum many-body system is modified in response to weak-to-moderate perturbations within a nonperturbative typicality framework. A key role is played by the so-called perturbation profile, which characterizes the dependence of the perturbation matrix elements in the eigenbasis of the unperturbed Hamiltonian on the difference of the corresponding energy eigenvalues. In particular, a banded matrix structure is quantitatively captured by a perturbation profile which approaches zero for large energy differences. The temporal modification of the relaxation is linked to the perturbation profile via a nonlinear integral equation, which admits approximate analytical solutions for sufficiently weak and strong perturbations, and for which we work out a numerical solution scheme in the general case. As an example, we consider a spin lattice model with a pronounced banded matrix structure, and we find very good agreement of the numerics with our analytical predictions without any free fit parameter.
