Mario Encinosa

Curvature-induced toroidal bound states

Curvature-induced bound-state eigenvalues and eigenfunctions for a particle constrained to move on the surface of a torus are calculated. A limit on the number of bound states that a torus with minor radius a and major radius R can support is obtained. A condition for mapping constrained particle wave functions on the torus into free particle wave functions is established.

Fourier Series Representation of Low-Lying Eigenfunctions for a Particle on the Torus

A Fourier series method for finding the low-lying eigenfunctions and eigenvalues of the Schrödinger equation for a particle on the surface of a torus is given.

Surface distortion effects on quantum dot helium

The Schrodinger equation for a quantum mechanical particle constrained to a surface includes a potential term dependent on surface curvature. We use differential forms to derive this term and employ Monge representations for two surfaces to obtain specific expressions for the potential. We calculate the first order perturbative effect of this potential on the ground state energy of model quantum dot helium. We find that the energy shift can be sensitive to the detailed shape of the surface distortion. This dependence arises from the Coulomb repulsion between the electron pair, which causes each electron to preferentially sample (or not sample) regions where physical curvature leads to comparatively large values of the distortion potential.

Electron wave functions on T2 in a static magnetic field of arbitrary direction

Abstract A basis set expansion is performed to find the eigenvalues and wave functions for an electron on a toroidal surface T 2 subject to a constant magnetic field in an arbitrary direction. The evolution of several low-lying states as a function of field strength and field orientation is reported, and a procedure to extend the results to include two-body Coulomb matrix elements on T 2 is presented.

Surface geometric effects on tunneling rates

A simple ballistic transport model is employed to investigate the effects of surface distortion on the tunneling spectrum of a model nanostructure. It is shown that constraining a particle to the curved surface of a nanostructure can have a significant influence on the tunneling spectrum of the system.

Quantum toroidal moments of nanohelix eigenstates

Developments in the area of metamaterial research have generated interest in toroidal moments and their treatment in the quantum regime. A quantum mechanical method of determining toroidal moments due to current circulating on a toroidal helix is presented. The Hamiltonian of a negatively charged spinless particle constrained to motion in the vicinity of a toroidal helix having loops of arbitrary eccentricity is developed. The resulting three dimensional Schr¨odinger equation is reduced to a one dimensional form inclusive of curvature effects. Low-lying eigenfunctions of the toroidal helix system are determined along with corresponding toroidal moments. A disagreement, not predicted by a classical treatment, arises between toroidal moments of elliptic toroidal helix systems when vertical and horizontal eccentricity are transposed.

Quantum electron transport in toroidal carbon nanotubes with metallic leads

A recursive Greens function method is employed to calculate the density-of-states, transmission function, and current through a 150 layer (3,3) armchair nanotorus (1800 atoms) with laterally attached metallic leads as functions of relative lead angle and magnetic flux. Plateaus in the transmissivity through the torus occur over wide ranges of lead placement, accompanied by enhancements in the transmissivity through the torus as magnetic flux normal to the toroidal plane is varied.

A numerical study of the spectrum and eigenfunctions on a tubular arc

Abstract The Hamiltonian for a particle constrained to move on the surface of a curved nanotube is derived using the methods of differential forms. A two-dimensional Gram–Schmidt orthonormalization procedure is employed to calculate basis functions for determining the eigenvalues and eigenstates of a tubular arc (a nanotube in the shape of a hyperbolic cosine) with several hundred scattering centers. The curvature of the tube is shown to induce bound states that are dependent on the curvature parameter and bend location of the tube.

Guided random-walk calculation of energies and 〈 r 2 〉 values of the 1 Σ g state of H 2 in a magnetic field

Energies and spatial observables for the

ENERGY SHIFTS RESULTING FROM SURFACE CURVATURE OF QUANTUM NANOSTRUCTURES

{}^{1}{\ensuremath{\Sigma}}_{g}