The Goldman symplectic form on the PGL(V)-Hitchin component

This article is the second of a pair of articles about the Goldman symplectic form on the PGL(V )-Hitchin component. We show that any ideal triangulation on a closed connected surface of genus at least 2, and any compatible bridge system determine a symplectic trivialization of the tangent bundle to the Hitchin component. Using this, we prove that a large class of flows defined in the companion paper [SWZ17] are Hamiltonian. We also construct an explicit collection of Hamiltonian vector fields on the Hitchin component that give a symplectic basis at every point. These are used to show that the global coordinate system on the Hitchin component defined iin the companion paper is a global Darboux coordinate system.Comment: 95 pages, 24 figures, Citations update

Double Andreev Reflections in Type-II Weyl Semimetal-Superconductor Junctions

We study the Andreev reflections (ARs) at the interface of the type-II Weyl semimetal-superconductor junctions and find double ARs when the superconductor is put in the Weyl semimetal band tilting direction, which is similar to the double reflections of light in anisotropic crystals. The directions of the double (retro and specular) ARs are symmetric about the normal due to the hyperboloidal Fermi surface near the Weyl nodes, but with different AR amplitudes depending on the direction and energy of the incident electron. When the normal direction of the Weyl semimetal-superconductor interface is changed from parallel to perpendicular with the tilt direction, the double ARs gradually evolve from one retro-AR and one specular AR, passing through double retro-ARs, one specular AR and one retro-AR, into one retro AR and one normal reflection, resulting in an anisotropic conductance which can be observed in experiments.Comment: 12 pages, 7 figure

Operator fidelity susceptibility: an indicator of quantum criticality

We introduce the operator fidelity and propose to use its susceptibility for characterizing the sensitivity of quantum systems to perturbations. Two typical models are addressed: one is the transverse Ising model exhibiting a quantum phase transition, and the other is the one dimensional Heisenberg spin chain with next-nearest-neighbor interactions, which has the degeneracy. It is revealed that the operator fidelity susceptibility is a good indicator of quantum criticality regardless of the system degeneracy.Comment: Four pages, two figure

Synthesis, Physical Properties and Biradical Characters of Zethrene-based Polycylic Hydrocarbons

Ph.DDOCTOR OF PHILOSOPH