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M. Encinosa

Publications and source records attributed to M. Encinosa.

13 recordsLinked to original sources
arXiv2011

Toroidal moments of Schrödinger eigenstates

The Hamiltonian for a particle constrained to motion near a toroidal helix with loops of arbitrary eccentricity is developed. The resulting three dimensional Schrödinger equation is reduced to a one dimensional effective equation inclusive of curvature effects. A basis set is employed to find low-lying eigenfunctions of the helix. Toroidal moments corresponding to the individual eigenfunctions are calculated. The dependence of the toroidal moments on the eccentricity of the loops is reported. Unlike the classical case, the moments strongly depend on the details of loop eccentricity.

quant-ph↗
arXiv2011

Quantum toroidal moments of an elliptic toroidal helix in a constant magnetic field

An effective one-dimensional Schrödinger equation for a spinless particle constrained to motion near a toroidal helix immersed in an arbitrarily oriented constant magnetic field is developed. The dependence of the induced toroidal moments on the magnetic flux through the helix is presented. The magnitude of the moments depend strongly on the component of the field normal to the toroidal plane. A strong dependence on coil eccentricity is also indicated. It is also shown that field-curvature coupling potential terms are necessary to preserve the Hermiticity of the minimal prescription Hamiltonian.

quant-ph↗
arXiv2006

Excitation of surface dipole and solenoidal modes on toroidal structures

The time dependent Schrodinger equation inclusive of curvature effects is developed for a spinless electron constrained to motion on a toroidal surface and subjected to circularly polarized and linearly polarized waves in the microwave regime. A basis set expansion is used to determine the character of the surface currents as the system is driven at a particular resonance frequency. Surface current densities and magnetic moments corresponding to those currents are calculated. It is shown that the currents can yield magnetic moments large not only along the toroidal symmetry axis, but along directions tangential and normal to the toroidal surface as well.

physics.class-ph↗
arXiv2005

Coupling curvature to a uniform magnetic field; an analytic and numerical study

The Schrodinger equation for an electron near an azimuthally symmetric curved surface $Σ$ in the presence of an arbitrary uniform magnetic field $\mathbf B$ is developed. A thin layer quantization procedure is implemented to bring the electron onto $Σ$, leading to the well known geometric potential $V_C \propto h^2-k$ and a second potential that couples $A_N$, the component of $\mathbf A$ normal to $Σ$ to mean surface curvature, as well as a term dependent on the normal derivative of $A_N$ evaluated on $Σ$. Numerical results in the form of ground state energies as a function of the applied field in several orientations are presented for a toroidal model.

quant-ph↗
arXiv2005

Elliptical torii in a constant magnetic field

The Schrodinger equation for an electron on the surface of an elliptical torus in the presence of a constant azimuthally symmetric magnetic field is developed. The single particle spectrum and eigenfunctions as a function of magnetic flux through the torus are determined and it is shown that inclusion of the geometric potential is necessary to recover the limiting cases of vertical strip and flat ring structures.

quant-ph↗
arXiv2005

On the geometric potential derived from Hermitian momenta on a curved surface

A geometric potential $V_C$ depending on the mean and Gaussian curvatures of a surface $Σ$ arises when confining a particle initially in a three-dimensional space $Ω$ onto $Σ$ when the particle Hamiltonian $H_Ω$ is taken proportional to the Laplacian $L$ on $Ω$. In this work rather than assume $H_Ω\propto L$, momenta $P_η$ Hermitian over $Ω$ are constructed and used to derive an alternate Hamiltonian $H_η$. The procedure leading to $V_C$, when performed with $H_η$, is shown to yield $V_C = 0$. To obtain a measure of the difference between the two approaches, numerical results are presented for a toroidal model.

quant-ph↗
arXiv2005

Electron wave functions on $T^2$ in a static magnetic field of arbitrary direction

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.

physics.comp-ph↗
arXiv2005

A note regarding Gram-Schmidt states on $T^2$

An efficient procedure for generating Gram-Schmidt states on a toroidal surface $T^2$ is presented. As an application of the method, low-lying eigenvalues and wave functions for an electron on $T^2$ subjected to a constant magnetic field are determined.

physics.comp-ph↗
arXiv2004

Wave functions in the neighborhood of a toroidal surface; hard vs. soft constraint

The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint $q \to 0$ limit, with $q$ the degree of freedom normal to the surface. In this work the hard constraint is relaxed, and eigenvalues and wave functions are numerically determined for a particle confined to a thin layer in the neighborhood of a toroidal surface. The hard constraint and finite layer (or soft constraint) quantities are comparable, but both differ markedly from those of the corresponding two dimensional system, indicating that the curvature potential continues to influence the dynamics when the particle is confined to a finite layer. This effect is potentially of consequence to the modelling of curved nanostructures.

quant-ph↗
arXiv2003

Bohmian trajectories on a toroidal surface

Bohmian trajectories on the toroidal surface T^2 are determined from eigenfunctions of the Schrodinger equation. An expression for the monodromy matrix M(t) on a curved surface is developed and eigenvalues of M(t) on T^2 calculated. Lyapunov exponents for trajectories on T^2 are found for some trajectories to be of order unity.

quant-ph↗
arXiv2003

Curvature induced toroidal bound states

Curvature induced bound state (E < 0) 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 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.

quant-ph↗
arXiv1999

Quantum particle constrained to a curved surface in the presence of a vector potential

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 term arises that couples the component of the vector potential normal to the surface to the mean curvature of the surface.

quant-ph↗