Research Projects

One of the fundamental goal of physics is to predict properties of a physical system under time evolution. Even if one knows the basic dynamical laws of physics it is often difficult to predict the time evolution of a complex system due to computational complexity; moreover the time evolution of such a complex system under different controlled conditions can reveal fundamental characteristics of the system that is otherwise inaccessible; and perhaps more interestingly  complex systems can be guided to evolve into a desirable and exotic state of matter. In this proposal we weave these three themes together towards understanding three different class of problems that are of great topical interest in quantum many body physics. We divide our investigations in this proposal into four themes as detailed below: 1) In the first theme we plan to probe the statics and dynamics of quasiperiodic(QP) and disordered systems. QP systems are often considered as a template for studying translational symmetry broken systems, recent works have revealed that such systems are unique. QP systems have useful properties and unprecedented control in experiments that made them interesting. In this project we plan to study dynamical charecteristics in and out of equilibrium settings, relevant to the state of the art experiments and to subtle theoretical issues that can be only explored in such systems. We plan to explore the dynamics in chiral disordered systems, while the proposed problems in this are well known but they have been postponed due to technical limitations, that we plan to study in this proposal. 2) In the second theme we plan to study dynamical properties of topological quantum matter. Topological quantum matter have been proposed and detected in 1D and in FQHE, but in the very promising direction (due to experimental abundance and manuaverability) of quantum spin liquids a smoking gun signature is still elusive. In this proposal we plan to use dynamical probes in search of clear-cut and charecteristics signature of fractional quaisparticles in quantum spin liquids. 3)In recent time a quantum bound on the lyapunov exponent was conjectured. It is believed that the bound has a classical origin, that lead to re-investigation of classical chaos in thermal many body systems. In this proposal we propose a study in non-linear system that can can be maximally chaotic due their classical charecteristics. 4)In the fourth theme we propose developement of computational techniques that will be useful for the problems proposed in previous themes but also expected to be useful to an wider range of problems. Two particular issues in computing real time dynamics of quantum many body systems of interest in this proposal is the precision problem and exponential resource problem. We plan to investigate high precision methods and employ machine learning techniques to solve this issues. We further propose a work on semiclassical molecular dynamics for the third theme.