Related papers: Curvature-induced quantum behaviour on a helical n…
We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…
Quasi-two-dimensional systems may exibit curvature, which adds three-dimensional influence to their internal properties. As shown by da Costa \cite{dacosta}, charged particles moving on a curved surface experience a curvature-dependent…
The curvature effect on the electronic states of a deformed cylindrical conducting surface of variable diameter is theoretically investigated. The quantum confinement of electrons normal to the curved surface results in an effective…
We derive the effective dimensionally reduced Sch\"odinger equation for electrons in strain-driven curved nanostructures by adiabatic separation of fast and slow quantum degrees of freedom. The emergent strain-induced geometric potential…
Since electrons in a ballistic regime perceive a carbon nanotube or a graphene layer structure as a continuous medium, we can use the study of the quantum dynamics of one electron constrained to a curve or surface to obtain a qualitative…
In this paper, we investigate the Schr\"odinger equation in a three-dimensional helically twisted space characterized by a non-trivial torsion parameter. By applying exact separation of variables, we derive the radial equation governing the…
The geometric potential in quantum mechanics has been attracted attention recently, providing a formalism to investigate the influence of curvature in the context of low-dimensional systems. In this paper, we study the consequences of a…
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…
Constraints play an important role in dynamical systems. However, the subtle effect of constraints in quantum mechanics is not very well studied. In the present work we concentrate on the quantum dynamics of a point particle moving on a…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
In classical mechanics, a nonrelativistic particle constrained on an $N-1$ curved hypersurface embedded in $N$ flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of…
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…
In this paper we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential. Suggesting that the quantum ring is affected by the…
A particle that is constrained to freely move on a hyperspherical surface in an $N\left( \geq 2\right) $ dimensional flat space experiences a curvature-induced gauge potential, whose form was given long ago (J. Math. Phys.…
The measured electric resistance of carbon nanotubes wrapped with DNA molecules depends strongly on the spin of the injected electrons. Motivated by these experiments, we study the effect of helix-shaped potentials on the electronic…
We review the classical and quantum singularity structure of a broad class of spacetimes with asymptotically power-law behavior near the origin. Quantum considerations "heal" a large class of scalar curvature singularities.
Twisted cylindrical tubes are important model systems for nanostructures, heterostructures, and curved quantum devices. In this work, we investigate the quantum behavior of an electron confined to a twisted cylindrical surface. By first…
The conductance of a ballistic elliptically shaped quantum wire is investigated theoretically. It is shown that the effect of the curvature results in strong oscillating dependence of the conductance on the applied bias.
We use an exact solution of the elastic membrane shape equation, representing the curvature, which will serve as a quantum potential in the quantum mechanical two dimensional Schrodinger equation for a (quasi-) particle on the surface of…
The quantum free particle on the sphere $S_\kappa^2$ ($\kappa>0$) and on the hyperbolic plane $H_\kappa^2$ ($\kappa<0$) is studied using a formalism that considers the curvature $\k$ as a parameter. The first part is mainly concerned with…