arXiv subjects
Publications and source records attributed to Yuqing Zhang.
In this paper, by using a powerful criterion for permutation polynomials given by Zieve, we give several classes of complete permutation monomials over $\F_{q^r}$. In addition, we present a class of complete permutation multinomials, which is a generalization of recent work.
The transmission spectrum of two dipole-dipole coupled atoms interacting with a single-mode optical cavity in strong coupling regime is investigated theoretically for the lower and higher excitation cases, respectively. The dressed states containing the dipole-dipole interaction (DDI) are obtained by transforming the two-atom system into an effective single-atom one. We found that the DDI can enhance the effects resulting from the positive atom-cavity detunings but weaken them for the negative detunings cases for lower excitation, which can promote the spectrum exhibiting two asymmetric peaks and shift the heights and the positions of them. For the higher excitation cases, DDI can augment the atomic saturation and lead to the deforming of the spectrum. Furthermore, the large DDI can make the atom and the cavity decouple, making a singlet of the normal-mode spectrum.
We consider multiparameter dynamics on the space of unimolular lattices. Along with quantitative nondivergence we prove that multiplicative Diophantine exponents of hyperplanes are inherited by their nondegenerate submanifolds.
We consider skew product extension of irrational rotations on the circle by $\Z^2$ determined by an integer valued function as well as a fixed point on the circle. We study ergodic components of such extension.
We study multiplicative Diophantine approximation property of vectors and compute Diophantine exponents of hyperplanes via dynamics.
We apply nondivergence estimates for flows on homogeneous spaces to compute Diophantine exponents of affine subspaces of $\R^n$ and their nondegenerate submanifolds.