Polaron dynamics with a multitude of Davydov D2_2 trial states

We propose an extension to the Davydov D$_2$ Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the "multi-D$_2$ Ansatz" is a linear combination of Davydov D$_2$ trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schr\"odinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D$_1$ and D$_2$ Ans\"atze. With an increase in the number of the Davydov D$_2$ trial states in the multi-D$_2$ Ansatz, deviation from the exact Schr\"odinger dynamics is gradually diminished, leading to a numerically exact solution to the Schr\"odinger equation.Comment: 14 pages, 15 figure

Geometric characterization on the solvability of regulator equations

The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The ‘feedback’ part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility. Useful results, such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds, are also obtained

Environmental regulation, innovation quality and firms’ competitivity-Quasi-natural experiment based on China’s carbon emissions trading pilot

In the study of the “Porter Hypothesis”, scholars explored the impact of different forms of innovation on the firms’ competitivity, but did not distinguish between innovations on the difference in patent quality. In addition, relevant research only regards innovation as a mediator between environmental regulation and competitivity, and doesn’t take into account innovation induced by environmental regulation, can only promote competitivity under the constraints of environmental regulation. That is to say, environmental regulation not only induces innovation, but also moderates innovation to promote competitivity. In view of this, we use panel data of A-share listed firms in China from 2006 to 2016, and adopt propensity score matching and different in different (PSM-DID) model to empirically test the inductive effect and moderating effect. The results show that CETS cannot only improve the quantity and quality, but also significantly enhance the firms’ market value; innovation itself cannot enhance the firms’ market value, but the interaction with CETS can promote the firms’ market value. In addition, the CETS has a stronger inductive effect on innovation of state-owned shares firms, but the positive moderating effect on high-quality innovation and competitivity only exists in non-state-owned shares firms