Effects of geometry and topology on some quantum mechanical systems

Thermal radiation in non-static curved spacetimes: quantum mechanical path integrals and configuration space topology

A quantum mechanical path integral derivation is given of a thermal propagator in non-static Gui spacetime. The thermal nature of the propagator is understood in terms of homotopically non-trivial paths in the configuration space appropriate to tortoise coordinates. The connection to thermal emission from collapsing black holes is discussed.

光机械超晶格中的非厄米拓扑与纠缠

Non-hermitian topology and entanglement in an optomechanical superlattice

本文提出一种光机械超晶格方案，利用空间调制驱动与耗散产生拓扑非平庸态，并证明其端态中力学与光学自由度纠缠对非零温度热库具有鲁棒性。

Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial

Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic, electromagnetic and mechanical transport properties across a wide range of systems, from cold atoms to metamaterials, active matter and geophysical flows. Recently, the advent of non-Hermitian topological systems---wherein energy is not conserved---has sparked considerable theoretical advances. In particular, novel topological phases that can only exist in non-Herm…

The influence of geometry and topology of quantum graphs on their nonlinear-optical properties

We analyze the nonlinear optics of quasi one-dimensional quantum graphs and manipulate their topology and geometry to generate for the first time nonlinearities in a simple system approaching the fundamental limits of the first and second hyperpolarizabilities. Changes in geometry result in smooth variations of the nonlinearities. Topological changes between geometrically-similar systems cause profound changes in the nonlinear susceptibilities that include a discontinuity due to abrupt changes in the boundary conditions. This work may inform the design of new molecules or nano- scale structure…

Geometry and topology of CC and CQ states

We show that multipartite mixed bipartite CC and CQ states are geometrically and topologically distinguished in the space of states. They are characterized by non-vanishing Euler-Poincaré characteristics on the topological side and by the existence of symplectic structure on the geometric side.

Topology shared between classical metamaterials and interacting superconductors

Supersymmetry has been studied at a linear level between normal modes of metamaterials described by rigidity matrices and non-interacting quantum Hamiltonians. The connection between classical and quantum was made through the matrices involved in each problem. Recently, insight into the behavior of nonlinear mechanical systems was found by defining topological indices via the Poincaré-Hopf index. It turns out, because of the mathematical similarity, this topological index shows a way to approach supersymmetric quantum theory from classical mechanics. Using this mathematical similarity, we esta…