arXiv subjects

G. Q. Wang

Publications and source records attributed to G. Q. Wang.

3 recordsLinked to original sources

arXiv2026

Dynamics of Dissipative Nonlinear Systems: A Study via 2D CGLE by Contact Geometry

We develop a contact-geometric framework for dissipative nonlinear field theories by extending the least constraint theorem to complex fields and establishing a rigorous link with probability measures. The Complex Ginzburg-Landau Equation serves as a paradigmatic example, yielding a dissipative Contact Hamilton-Jacobi equation that governs the evolution of the action functional. Through canonical transformation and travelling-wave reduction, exact Jacobi elliptic solutions are obtained, revealing a continuous transition from periodic periodons to localised solitons. Probabilistic analysis identifies a universal switching line separating dynamical regimes and uncovers a first-order periodon-soliton phase transition with a hysteresis loop. The conserved contact potential emerges as the key geometric quantity governing pattern formation in dissipative media, analogous to energy in conservative systems.

nlin.PS↗

arXiv2024

Least Constraint and Contact Dynamics of Stochastic Vector Bundles

This paper investigates the contact structures and dynamics of stochastic vector bundles, leading to the formulation of the least constraint theorem. It is found that the probability space of stochastic vector bundles possesses an infinite-order jet structure, which enables the geometric analysis of stochastic processes. Furthermore, this study demonstrates that stochastic vector bundles have a natural contact structure, leading to the decomposition of the tangent space and providing insight into the evolution and constraints of the system. Finally, we derive a set of contact dynamical equations for the stochastic vector bundles. These equations correspond to the least constraint on the evolution of stochastic vector bundles, which is a counterpart to the least action principle for symplectic structures. This shows the relationship between the geometric structure of the stochastic system evolution and its tendency to minimize constraints. This study provides a geometric framework for analyzing stochastic space with potential applications in various fields where probabilistic behavior is crucial.

math-ph↗

arXiv2018

Strain-controlled valley and spin separation in silicene heterojunctions

We adopt the tight-binding mode-matching method to study the strain effect on silicene heterojunctions. It is found that valley- and spin-dependent separation of electrons cannot be achieved by the electric field only. When a strain and an electric field are simultaneously applied to the central scattering region, not only are the electrons of valleys K and K' separated into two distinct transmission lobes in opposite transverse directions, but the up-spin and down-spin electrons will also move in the two opposite transverse directions. Therefore, one can realize an effective modulation of valley- and spin-dependent transport by changing the amplitude and the stretch direction of the strain. The phenomenon of the strain-induced valley and spin deflection can be exploited for silicene-based valleytronics devices.

cond-mat.mes-hall↗