Dynamical properties of one dimensional strongly correlated many-particle systems

目前设想了两条工作路线。第一个方案是关于开放的多粒子量子系统的非平衡动力学。这些可以方便地用所谓的林德布拉德方程来描述。一个普遍的问题是，LE是很难分析的数值或分析手段。最近已经证明，在特定的例子Lindblad方程可以映射到非埃尔米特可积模型。这为可积模型技术在此类问题上的应用提供了可能性，并为开放的相互作用多粒子量子系统建立了精确的解决范式。这个项目是在EPSRC的大挑战领域“涌现和物理远离平衡”。在项目的第一部分中，将获得先前研究的示例Hubbard模型的两点和四点函数的时间演化的精确结果。在第二部分中，我们将分析其他Lindblad方程，目的是将它们映射到具有非平凡稳态的非厄米特可积哈密顿量。第二部分工作是关于准一维量子磁体SrCo 2V 2O 8上的非弹性中子散射实验的理论建模，其最近显示出将拓扑激发限制在类介子束缚态中。一个悬而未决的问题是弱三维耦合的影响。即将进行的实验将测量垂直于链方向的色散关系，这将使得有可能确定链间耦合的函数形式。一旦实现了这一点，链间耦合效应可以通过结合现有的结果与矩阵随机相位近似进行分析。这样的理论分析的结果，然后可以比较现有的非弹性中子散射数据。

At present two lines of work are envisaged. The first programme is concerned with non-equilibrium dynamics in open many-particle quantum systems. These can be conveniently described by so-called Lindblad equations. A general problem is that LE are difficult to analyse by either numerical or analytical means. It has been recently demonstrated that in particular examples Lindblad equations can be mapped onto non-hermitian integrable models. This opens up the possibility to bring integrable model techniques to bear on such problems and establish exactly solved paradigms of open interacting many-particle quantum systems. This project is squarely in the EPSRC grand challenge area "Emergence and Physics Far From Equilibrium". In the first part of the project exact results for the time evolution of two and four point functions will be obtained for the previously studied example imaginary-U Hubbard model. In the second part of the project other Lindblad equations will be analyzed with the objective of mapping them to non-herminitian integrable Hamiltonians, that have non-trivial steady states.The second line of work is concerned with the theoretical modelling of inelastic neutron scattering experiments on the quasi-one dimensional quantum magnet SrCo2V2O8, which has been recently shown to exhibit confinement of topological excitations into meson-like bound states. An open problem are the effects of the weak three-dimensional couplings. Forthcoming experiments will measure the dispersion relations perpendicular to the chain direction, which will make it possible to determine the functional form of the interchain couplings. Once this has been achieved, the interchain coupling effects can be analyzed by combining existing results with a matrix random phase approximation. The result of such a theoretical analysis can then be compared to available inelastic neutron scattering data.