arXiv subjects

Guo-Hua Liang

Publications and source records attributed to Guo-Hua Liang.

13 recordsLinked to original sources

arXiv2025

Quantum States in Twisted Tubes with Linear Cross-Section Variation

We study the quantum dynamics of a particle confined in a twisted tube with a linearly varying cross section. By relating a general linear transformation matrix to the system's Hamiltonian, we use an extended thin-layer method to derive an effective Hamiltonian for tangential motion under mild and general linear transformations. Explicit forms are provided for three fundamental transformations: rotation, scaling, and shearing. Rotation introduces a gauge field coupled to angular momentum, while scaling and shearing produce geometric potentials that lift degeneracies in non-circular cross sections. In square cross sections, these transformations cause energy splittings among formerly degenerate states, whereas circular cross sections retain degeneracy. Through an example combining rotation and squeezing, we analyze state evolution and compute the quantum geometric tensor to quantify geometric response. Our results demonstrate how geometric transformations can tailor quantum states and suggest that circular waveguides are more robust against mode mixing.

quant-ph↗

arXiv2025

Spin textures in curved paths on a curved surface

This study investigates the quantum dynamics of a spin-1/2 particle confined to a curved path from the dynamics of a two-dimensional curved thin-layer system incorporating spin connection contributions. We demonstrate that the geodesic curvature, normal curvature, and geodesic torsion govern the emergent non-Abelian gauge potential, while the geodesic and Gaussian curvatures govern the effective scalar potential in the Hamiltonian. The resulting spin precession dynamics induced by the gauge potential are analyzed with and without the adiabatic approximation. Under this approximation, the surface topology is linked to the rotation angle of spin orientation along a surface boundary and to the pseudo-magnetic flux. Spin texture evolution along helices illustrates distinct behaviors under geodesic versus non-geodesic propagation. Furthermore, the spin evolution along Viviani's curve exemplifies surface dependence. The curve's topology ensures closure of the spin direction and independence of the spin from the path direction. Our theory establishes a framework for spin-state manipulation via engineered nanostructured channels, enabling novel topological quantum control strategies.

quant-ph↗

arXiv2022

Effective quantum dynamics in curved thin-layer system with inhomogeneous confinement

The motion of quantum particles homogeneously constrained to a curved surface is affected by a curvature induced geometric potential. Here, we consider the case of inhomogeneous confinement and derive the effective Hamiltonian by extending thin-layer procedure, where an extra effective potential appears. This effective potential is relevant to the ground state energy perpendicular to the surface and the morphology of the confining potential. Tiny changes in the thickness are envisioned to induce considerable magnitude of the effective potential. To demonstrate the impact of the inhomogeneity, we apply our method to investigate the coherent transport on a cylindrical surface where a confining potential with two helical ditches is imposed. Numerical analysis reveals that the inhomogeneity of the confinement significantly changes the transport properties. This study develops the method for low-dimensional constrained systems and exhibits the possibility of new degree of control for waveguiding in nanostructures.

quant-ph↗

arXiv2021

Quantum mechanics of fermion confined to a curved surface in Foldy-Wouthuysen representation

In Foldy-Wouthuysen representation, we deduce the effective quantum mechanics for a particle confined to a curved surface by using the thin-layer quantization scheme. We find that the spin effect caused by confined potential as the results of relativistic correction in the non-relativistic limit. Furthermore, the spin connection appeared in curved surface which depends on curvature contributes a Zeeman-like gap in the relativistic correction term. In addition, the confined potential also induces a curvature-independent energy shift, which is from the zitterbewegung effect. As an example, we apply the effective Hamiltonian to torus surface, in which we obtain expectantly the spin effects related to confined potential. Those results directly demonstrate the scaling of the uncommutation of the non-relativistic limit and the thin-layer quantization formalism

quant-ph↗

arXiv2020

Effective dynamics for a spin-1/2 particle constrained to a space curve in an electric and magnetic field

We consider the dynamics of a spin-1/2 particle constrained to move in an arbitrary space curve with an external electric and magnetic field applied. With the aid of gauge theory, we successfully decouple the tangential and normal dynamics and derive the effective Hamiltonian. A new type of quantum potential called SU(2) Zeeman interaction appears, which is induced by the electric field and couples spin and intrinsic orbital angular momentum. Based on the Hamiltonian, we discuss the spin precession for zero intrinsic orbital angular momentum case and the energy splitting caused by the SU(2) Zeeman interaction for a helix as examples, showing the combined effect of geometry and external field. The new interaction may bring new approaches to manipulate quantum states in spintronics.

cond-mat.mes-hall↗

arXiv2020

Spin polarization of electrons through corrugated surface in magnetic field

Noninteracting electrons confined to a corrugated surface are investigated in magnetic field, and the associated effective Pauli equation is given analytically by the thin-layer quantization scheme. Interestingly, the Zeeman splitting gaps can be adjusted by curvature, and there is a geometric potential induced by curvature. Further, we discuss the spin-dependent transport properties for confined electrons by numerical calculation. More interestingly, we find that the spin polarization induced by curvature becomes substantial when the incident energy has small value. The results are considerable for a spin transistor with small spin current.

cond-mat.mes-hall↗

arXiv2019

Geometrical phase and Hall effect associated with the transverse spin of light

By analyzing the vectorial Helmholtz equation within the thin-layer approach, we find that light acquires a novel geometrical phase, in addition to the usual one (the optical Berry phase), during the propagation along a curved path. Unlike the optical Berry phase, the novel geometrical phase is induced by the transverse spin along the binormal direction and associated with the curvature of the curve. Furthermore, we show a novel Hall effect of light induced by the torsion of the curve and associated with the transverse spin along the binormal direction, which is different from the usual spin Hall effect of light. Finally, we demonstrate that the usual and novel geometrical phase phenomena are described by different geometry-induced U(1) gauge fields in different adiabatic approximations. In the nonadiabatic case, these gauge fields are united in one effective equation by SO(3) group.

physics.optics↗

arXiv2018

Pseudo-magnetic field and effective spin-orbit interaction for a spin-1/2 particle confined to a curved surface

By considering the spin connection, we deduce the effective equation for a spin-1/2 particle confined to a curved surface with the non-relativistic limit and in the thin-layer quantization formalism. We obtain a pseudo-magnetic field and an effective spin-orbit interaction generated by the spin connection. Geometrically, the pseudo-magnetic field is proportional to the Gaussian curvature and the effective spin-orbit interaction is determined by the Weingarten curvature tensor. Particularly, we find that the pseudo-magnetic field and the effective spin-orbit interaction can be employed to separate the electrons with different spin orientations. All these results are demonstrated in two examples, a straight cylindrical surface and a bent one.

quant-ph↗

arXiv2018

Electromagnetic wave propagating along a space curve

Using the thin-layer approach, we derive the effective equation for the electromagnetic wave propagating along a space curve. We find intrinsic spin-orbit, extrinsic spin-orbit and extrinsic orbital angular momentum and intrinsic orbital angular momentum couplings induced by torsion, which can lead to geometric phase, spin and orbital Hall effects. And we show the helicity inversion induced by curvature that can convert the right-handed circularly polarized electromagnetic wave into left-handed polarized one, vice verse. Finally, we demonstrate that the gauge invariance of the effective dynamics is protected by the geometrically induced gauge potential.

physics.optics↗

arXiv2017

Spin-polarized transport in helical membranes due to spin-orbit coupling

The spin-dependent electron transmission through a helical membrane with account of linear spin-orbit interaction has been investigated by numerically solving the Schrödinger equation in cylindrical coordinates . It is shown that the spin precession is affected by the magnitude of geometric parameters and chirality of the membrane. This effect is also explained analytically by using the perturbation theory in the weak coupling regime. In the strong coupling regime, the current spin polarization is evident when the number of the open modes in leads is larger than that of the open channels in the membrane. Moreover, we find that the chirality of the helical membrane can determine the orientation of current spin polarization. Therefore, one may get totally opposite spin currents from the helical membranes rolled against different directions.

cond-mat.mes-hall↗

arXiv2016

Coherent electron transport in a helical nanotube

The quantum dynamics of carriers bound to helical tube surfaces is investigated in a thin-layer quantization scheme. By numerically solving the open-boundary Schr$\ddot{\rm o}$dinger equation in curvilinear coordinates, geometric effect on the coherent transmission spectra is analysed in the case of single propagating mode as well as multimode. It is shown that, the coiling endows the helical nanotube with different transport properties from a bent cylindrical surface. Fano resonance appears as a purely geometric effect in the conductance, the corresponding energy of quasibound state is obviously influenced by the torsion and length of the nanotube. We also find new plateaus in the conductance. The transport of double-degenerate mode in this geometry is reminiscent of the Zeeman coupling between the magnetic field and spin angular momentum in quasi-one-dimensional structure.

cond-mat.mes-hall↗

arXiv2016

Transmission gaps from corrugations

A model including a periodically corrugated thin layer with GaAs substrate is employed to investigate the effects of the corrugations on the transmission probability of the nanostructure. We find that transmission gaps and resonant tunneling domains emerge from the corrugations, in the tunneling domains the tunneling peaks and valleys result from the boundaries between adjacent regions in which electron has different effective masses, and can be slightly modified by the layer thickness. These results can provide an access to design a curvature-tunable filter.

cond-mat.mes-hall↗

arXiv2015

Curvature-induced bound states and coherent electron transport on the surface of a truncated cone

We study the curvature-induced bound states and the coherent transport properties for a particle constrained to move on a truncated cone-like surface. With longitudinal hard wall boundary condition, the probability densities and spectra energy shifts are calculated, and are found to be obviously affected by the surface curvature. The bound-state energy levels and energy differences decrease as increasing the vertex angle or the ratio of axial length to bottom radius of the truncated cone. In a two-dimensional (2D) GaAs substrate with this geometric structure, an estimation of the ground-state energy shift of ballistic transport electrons induced by the geometric potential (GP) is addressed, which shows that the fraction of the ground-state energy shift resulting from the surface curvature is unnegligible under some region of geometric parameters. Furthermore, we model a truncated cone-like junction joining two cylinders with different radii, and investigate the effect of the GP on the transmission properties by numerically solving the open-boundary 2D Schrödinger equation with GP on the junction surface. It is shown that the oscillatory behavior of the transmission coefficient as a function of the injection energy is more pronounced when steeper GP wells appear at the two ends of the junction. Moreover, at specific injection energy, the transmission coefficient is oscillating with the ratio of the cylinder radii at incoming and outgoing sides.

quant-ph↗