arXiv subjects

Chang-Tan Xu

Publications and source records attributed to Chang-Tan Xu.

3 recordsLinked to original sources

arXiv2019

The geometric potential of a double-frequency corrugated surface

For an electron confined to a surface reconstructed by double-frequency corrugations, we give the effective Hamiltonian by the formula of geometric influences, obtain an additive scalar potential induced by curvature that consists of attractive wells with different depth. The difference is generated by the multiple frequency of the double-frequency corrugation. Subsequently, we investigate the effects of geometric potential on the transmission probability, and find the resonant tunneling peaks becoming rapidly sharper and the transmission gaps being substantially widened with increasing the multiple frequency. As a potential application, double-frequency corrugations can be employed to select electrons with particular incident energy, as an electronic switch, which are more effective than a single-frequency ones.

cond-mat.mes-hall↗

arXiv2014

Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field

We derive the Pauli equation for a charged spin particle confined to move on a spatially curved surface $\mathcal{S}$ in an electromagnetic field. Using the thin-layer quantization scheme to constrain the particle on $\mathcal{S}$, and in the transformed spinor representations, we obtain the well-known geometric potential $V_g$ and the presence of $e^{-iφ}$, which can generate additive spin connection geometric potentials by the curvilinear coordinate derivatives, and we find that the two fundamental evidences in the literature [Giulio Ferrari and Giampaolo Cuoghi, Phys. Rev. Lett. 100, 230403 (2008).] are still valid in the present system without source current perpendicular to $\mathcal{S}$. Finally, we apply the surface Pauli equation to spherical, cylindrical, and toroidal surfaces, in which we obtain expectantly the geometric potentials and new spin connection geometric potentials, and find that only the normal Pauli matrix appears in these equations.

quant-ph↗

arXiv2013

The Dirac Conjecture and the Non-uniqueness of Lagrangian

By adding the total time derivatives of all the constraints to the Lagrangian step by step, we achieve the further work of the Dirac conjecture left by Dirac. Hitherto, the Dirac conjecture is proved completely. It is worth noticing that the addition of the total time derivatives to the Lagrangian can turn up some constraints hiding in the original Lagrangian. For a constrained system, the extended Hamiltonian $H_E$ considers more constraints, and shows symmetries more obviously than the total Hamiltonian $H_T$. In the Lagrangian formalism, we reconsider the Cawley counterexample, and offer an example in which in accordance with its original Lagrangian its extended Hamiltonian is better than its total Hamiltonian.

hep-th↗