A functional for the momentum equations of incompressible viscous flow

Vectorial mechanics and analytical mechanics are two time-honored forms of classical mechanics. Vectorial mechanics is mainly based on Newton’s l aws i n a c lear a nd simple mathematical form. It has achieved a high degree of sophistication and success in solid mechanics. Analytical mechanics is based on the principle of virtual work and D'Alembert’s principle, which is highly universal. Often, the term vectorial mechanics is applied to the form based on Newton's work, to contrast it with analytical mechanics which uses two scalar properties of motion, the kinetic and potential energies, instead of vector forces, to analyze the motions. Analytical mechanics was primarily developed to extend the scope of classical mechanics in a systematic, generalized and efficient way to solve problems using the concept of constraints on systems and path integrals. In this paper, we give a functional of fluid in Lagrangian form. Then we demonstrate that the momentum equations of incompressible viscous flow can be achieved after several mathematical operations. At last, we show the Eulerian approximation of the energy functional under some assumptions. Our work lays a good foundation for our numerical methods

Chiral topological excitonic insulator in semiconductor quantum wells

We present a scheme to realize the chiral topological excitonic insulator in semiconductor heterostructures which can be experimentally fabricated with a coupled quantum well adjacent to twoferromagnetic insulating films. The different mean-field chiral topological orders, which are due to the change in the directions of the magnetization of the ferromagnetic films, can be characterized by the TKNN numbers in the bulk system as well as by the winding numbers of the gapless states in the edged system. Furthermore, we propose an experimental scheme to detect the emergence of the chiral gapless edge state and distinguish different chiral topological orders by measuring the thermal conductance.Comment: 14 pages, 4 figure

Quantum Hall Effects in a Non-Abelian Honeycomb Lattice

We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a many-Dirac-points system. We find that the quantum Hall effects present different features as change as relative strengths of several perturbations. Namely, a gauge-field-dressed next-nearest-neighbor hopping can induce the quantum spin Hall effect and a Zeeman field can induce a so-called quantum anomalous valley Hall effect which includes two copies of quantum Hall states with opposite Chern numbers and counter-propagating edge states. Our study extends the borders of the field of quantum Hall effects in honeycomb optical lattice when the internal valley degrees of freedom enlarge.Comment: 7 pages, 6 figure