相关论文: Geometry-Induced Chiral Currents in a Mesoscopic H…

The recent experimental observations of the quantum Hall effect in 3D topological semimetals have attracted great attention, but there are still debates on its origin. We systematically study the dependence of the quantum Hall effect in…

Nonlinear frequency conversion unlocks technologies ranging from telecommunications to quantum computation; however, weak nonlinearities and architectures that resist miniaturization currently limit devices. Here, we combine a…

We combine a heuristic theory of geometric percolation and the Smoluchowski theory of colloid dynamics to predict the impact of shear flow on the percolation threshold of hard spherical colloidal particles, and verify our findings by means…

It was recently shown that tunneling wavefunction proposal is consistent with loop quantum geometry corrections including both holonomy and inverse scale factor corrections in the gravitational part of a spatially closed isotropic model…

The link between 3D spaces with (in general, non-constant) curvature and quantum deformations is presented. It is shown how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians that…

Let $(M, \partial M)$ be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. For each hyperbolic metric $g$ on $M$ such that $\dr M$ is smooth and strictly convex, the induced metric on $\dr M$…

The oscillation of tunnel splitting are obtained by geometrical analysis of the topological Wess-Zumino phase on the basis of tunneling paths in biaxial nanomagnetic particles with magnetic field along the hard anisotropy axis. This theory…

A magnetic domain boundary on the surface of a three-dimensional topological insulator is predicted to host a chiral edge state, but direct demonstration is challenging. Here, we used a scanning superconducting quantum interference device…

Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…

Magnetoresistance oscillations in semiconductor quantum wells, with the semi-parabolic plus semi-inverse squared potential, under the influence of intense electromagnetic waves (IEMW), is studied theoretically. Analytical expression for the…

We construct a metric structure on a configuration space of gauge connections and show that it naturally produces a candidate for a non-perturbative, 3+1 dimensional Yang-Mills-Dirac quantum field theory on a curved background. The metric…

This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random…

We establish a quantum dynamics framework for curved submanifolds embedded in higher-dimensional spaces. Through rigorous dimensional reduction, we derive the first complete Schr\"{o}dinger and Klein-Gordon equations incorporating…

Can geometry alone reshape equilibrium? Cascaded nanofluidic chambers show complex accumulation patterns, traditionally attributed to geometric diode effects. We use 3D molecular dynamics to decouple funnel rectification from boundary…

The strong chiral light-matter interaction is crucial for various important fields such as chiral optics, quantum optics, and biomedical optics, driving a quest for the extreme intrinsic chirality assisted by ultrahigh quality ($Q$-) factor…

The experimental progress in synthesizing low-dimensional nanostructures where carriers are confined to bent surfaces has boosted the interest in the theory of quantum mechanics on curved two-dimensional manifolds. It was recently asserted…

Devices exhibiting the integer quantum Hall effect can be modeled by one-electron Schroedinger operators describing the planar motion of an electron in a perpendicular, constant magnetic field, and under the influence of an electrostatic…

Two-dimensional Chern insulators have emerged as crucial platforms for the realization of the quantum anomalous Hall effect, and as such have attracted significant interest in spintronics and topological quantum physics due to their unique…

This thesis explores the application of differential geometric and general relativistic techniques to deepen our understanding of quantum mechanical systems. We focus on three systems, employing these mathematical frameworks to uncover…

Weyl fermions in an external magnetic field exhibit the chiral anomaly, a non-conservation of chiral fermions. In a Weyl semimetal, a spatially inhomogeneous Weyl node separation causes similar effect by creating an intrinsic…