arXiv subjects

W. K. Du

Publications and source records attributed to W. K. Du.

3 recordsLinked to original sources

arXiv2021

Local shape of the vapor-liquid critical point on the thermodynamic surface and the van der Waals equation of state

Differential geometry is powerful tool to analyze the vapor-liquid critical point on the surface of the thermodynamic equation of state. The existence of usual condition of the critical point $\left( \partial p/\partial V\right) _{T}=0$ requires the isothermal process, but the universality of the critical point is its independence of whatever process is taken, and so we can assume $\left( \partial p/\partial T\right) _{V}=0$. The distinction between the critical point and other points on the surface leads us to further assume that the critical point is geometrically represented by zero Gaussian curvature. A slight extension of the van der Waals equation of state is to letting two parameters $a$ and $b$ in it vary with temperature, which then satisfies both assumptions and reproduces its usual form when the temperature is approximately the critical one.

cond-mat.stat-mech↗

arXiv2019

No existence of the geometric potential for a Dirac fermion on two-dimensional curved surfaces of revolution

For a free particle that non-relativistically moves on a curved surface, there are curvature-induced quantum potentials that significantly influence the surface quantum states, but the experimental results in topological insulators, whenever curved or not, indicate no evidence of such a potential, implying that there does not exist such a quantum potential for the relativistic particles, constrained on the surface or not. Within the framework of Dirac quantization scheme, we demonstrate a general result that for a Dirac fermion on a two-dimensional curved surface of revolution, no curvature-induced quantum potential is permissible.

cond-mat.mes-hall↗

arXiv2019

General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere

For a particle that is constrained on an ($N-1$)-dimensional ($N\geq2$) curved surface, the Cartesian components of its momentum in $N$-dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of a Dirac fermion on a two-dimensional sphere and we show that there is the generalized total angular momentum whose three cartesian components form the $su(2)$ algebra, obtained before by consideration of dynamics of the particle, and we demonstrate that there is no curvature-induced geometric potential for the fermion.

hep-th↗