Moduli Spaces of Parabolic Bundles over $mathbb{P}^1$ with Five Marked Points

This paper considers the moduli spaces (stacks) of parabolic bundles (parabolic logarithmic flat bundles with given spectrum, parabolic regular Higgs bundles) with rank 2 and degree 1 over $mathbb{P}^1$ with five marked points. The stratification structures on these moduli spaces (stacks) are investigated. We confirm Simpsons foliation conjecture of moduli space of parabolic logarithmic flat bundles for our case.

General Formulas of the Structure Constants in the $mathfrak{su}(N)$ Lie Algebra

We provide the analytic expressions of the totally symmetric and anti-symmetric structure constants in the $mathfrak{su}(N)$ Lie algebra. The derivation is based on a relation linking the index of a generator to the indexes of its non-null elements. The closed formulas obtained to compute the values of the structure constants are simple expressions involving those indexes and can be analytically evaluated without any need of the expression of the generators. We hope that these expressions can be widely used for analytical and computational interest in Physics.

Theory of Vibrational Polariton Chemistry in the Collective Coupling Regime

We theoretically demonstrate that chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity-frequency modification of the rate constant. When a reaction coordinate is strongly coupled to the solvent molecules, the reaction rate constant is reduced due to the dynamical caging effect. We demonstrate that collectively coupling the solvent to the cavity can further enhance this dynamical caging effect, leading to additional suppression of the chemical kinetics. This effect is further amplified when cavity loss is considered.

Dual Synchronous Generator: Inertial Current Source based Grid-Forming Solution for VSC

In order to improve dynamic characteristics of the power system with high-proportion renewable energy sources (RESs), it is necessary for the voltage source converter (VSC), interfaces of RESs, to provide inertial and frequency regulation. In practical applications, VSCs are better to be controlled as a current source due to its weak overcurrent capacity. According to the characteristic, a dual synchronous theory is proposed to analyze the synchronization between current sources in this paper. Based on dual synchronous idea, a dual synchronous generator (DSG) control is applied in VSC to form inertial current source. In addition, a braking control is embedded in DSG control to improve the transient stability of VSC. Finally, experimental results verify the effectiveness of the theory and the control method.

Ab-initio Symmetric Quasi-Classical Approach to Investigate Molecular Tully Models

We perform on-the-fly non-adiabatic molecular dynamics simulations using the symmetrical quasi-classical (SQC) approach with the recently suggested molecular Tully models: ethylene and fulvene. We attempt to provide benchmarks of the SQC methods using both the square and the triangle windowing schemes as well as the recently proposed electronic zero-point-energy correction scheme (so-called the gamma correction). We use the quasi-diabatic propagation scheme to directly interface the diabatic SQC methods with adiabatic electronic structure calculations. Our results showcase the drastic improvement of the accuracy by using the trajectory-adjusted gamma-corrections, which outperform the widely used trajectory surface hopping method with decoherence corrections. These calculations provide useful and non-trivial tests to systematically investigate the numerical performance of various diabatic quantum dynamics approaches, going beyond simple diabatic model systems that have been used as the major workhorse in the quantum dynamics field. At the same time, these available benchmark studies will also likely foster the development of new quantum dynamics approaches based on these techniques.

Newton-based methods for finding the positive ground state of Gross-Pitaevskii equations

The discretization of Gross-Pitaevskii equations (GPE) leads to a nonlinear eigenvalue problem with eigenvector nonlinearity (NEPv). In this paper, we use two Newton-based methods to compute the positive ground state of GPE. The first method comes from the Newton-Noda iteration for saturable nonlinear Schrodinger equations proposed by Liu, which can be transferred to GPE naturally. The second method combines the idea of the Bisection method and the idea of Newton method, in which, each subproblem involving block tridiagonal linear systems can be solved easily. We give an explicit convergence and computational complexity analysis for it. Numerical experiments are provided to support the theoretical results.

Curvature formulas related to a family of stable Higgs bundles

In this paper, we investigate the geometry of the base complex manifold of an effectively parametrized holomorphic family of stable Higgs bundles over a fixed compact K{a}hler manifold. The starting point of our study is Schumacher-Toma/Biswas-Schumachers curvature formulas for Weil-Petersson-type metrics, in Sect. 2, we give some applications of their formulas on the geometric properties of the base manifold. In Sect. 3, we calculate the curvature on the higher direct image bundle, which recovers Biswas-Schumachers curvature formula. In Sect. 4, we construct a smooth and strongly pseudo-convex complex Finsler metric for the base manifold, the corresponding holomorphic sectional curvature is calculated explicitly.

Generalized Deligne-Hitchin Twistor Spaces: Construction and Properties

In this paper, we generalize the construction of Deligne-Hitchin twistor space by gluing two certain Hodge moduli spaces. We investigate such generalized Deligne-Hitchin twistor space as a complex analytic manifold, more precisely, we show it admits a global smooth trivialization such that the induced product metric is balanced, and it carries a semistable holomorphic tangent bundle. Moreover, we study the automorphism groups of the Hodge moduli spaces and the generalized Deligne-Hitchin twistor space.

Simpson Filtration and Oper Stratum Conjecture

In this paper, we prove that for the oper stratification of the de Rham moduli space $M_{mathrm{dR}}(X,r)$, the closed oper stratum is the unique minimal stratum with dimension $r^2(g-1)+g+1$, and the open dense stratum consisting of irreducible flat bundles with stable underlying vector bundles is the unique maximal stratum.

Finding the Global Optimum of a Class of Quartic Minimization Problem

We consider a special nonconvex quartic minimization problem over a single spherical constraint, which includes the discretized energy functional minimization problem of non-rotating Bose-Einstein condensates (BECs) as one of the important applications. Such a problem is studied by exploiting its characterization as a nonlinear eigenvalue problem with eigenvector nonlinearity (NEPv), which admits a unique nonnegative eigenvector, and this eigenvector is exactly the global minimizer to the quartic minimization. With these properties, any algorithm converging to the nonnegative stationary point of this optimization problem finds its global minimum, such as the regularized Newton (RN) method. In particular, we obtain the global convergence to global optimum of the inexact alternating direction method of multipliers (ADMM) for this problem. Numerical experiments for applications in non-rotating BEC validate our theories.