Dynamical properties of one dimensional strongly correlated many-particle systems

目前设想了两条工作路线。第一个程序涉及开放多粒子量子系统中的非平衡动力学。这些可以很方便地用所谓的Lindblad方程来描述。一个普遍的问题是，LE很难用数值或分析方法进行分析。最近已经证明，在特定的例子中，Lindblad方程可以映射到非厄米可积模型上。这为将可积模型技术应用于此类问题和建立开放相互作用多粒子量子系统的精确求解范式提供了可能。这个项目正好在EPSRC的重大挑战领域“新兴和物理远离平衡”。在本项目的第一部分中，我们将以之前研究过的虚U Hubbard模型为例，得到两点和四点函数随时间演化的精确结果。在项目的第二部分，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赫米特可积哈密顿量。第二部分工作涉及准一维量子磁体SrCo2V2O8上的非弹性中子散射实验的理论建模，最近显示出拓扑激发被限制为类介子束缚态。一个悬而未决的问题是弱三维耦合的影响。未来的实验将测量垂直于链方向的色散关系，这将使确定链间耦合的函数形式成为可能。一旦实现了这一点，就可以通过将现有结果与矩阵随机相位近似相结合来分析链间耦合效应。然后可以将这种理论分析的结果与现有的非弹性中子散射数据进行比较。

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.