Spin force and torque in non-relativistic Dirac oscillator on a sphere

Download

index.pdf

Date

2018-03-30

Author

Shikakhwa, M. S.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

279
views

71
downloads

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin-orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.

Subject Keywords

Spin hall effect, Spin force, Dirac oscillator, Spin-orbit coupling, Zitterbewegung

URI

https://hdl.handle.net/11511/63938

Journal

PHYSICS LETTERS A

DOI

https://doi.org/10.1016/j.physleta.2017.12.040

Collections

Natural Sciences and Mathematics, Article

Suggestions

OpenMETU
Core

Spin–orbit effects on the nonlinear optical properties of a quantum dot in simultaneous electric and magnetic fields Aytekin, O.; Turgut, Sadi; Tomak, Mehmet (Elsevier BV, 2014-11) We report on the nonlinear optical properties of a quantum dot including the Rashba spin-orbit interaction (RSOI) with external electric and magnetic fields. The effect of dot size is considered. We do not make any assumptions about the strength of the confinement. We use the numerical diagonalization of the Hamiltonian to determine the electronic structure. The confining potential is taken to be of the Woods-Saxon type. We find the effect of RSOI on nonlinear optical coefficients.
Exact solution of the time-dependent harmonic plus an inverse harmonic potential with a time-dependent electromagnetic field Yuce, C (2003-12-01) In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained.
Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates Shikakhwa, M. S.; Chair, N. (2016-08-19) The Schrodinger Hamiltonian of a spin-less particle as well as the Pauli Hamiltonian with spin-orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate are constructed. A new approach, based on the physical argument that upon squeezing the particle to the surface by a potential, then it is the physical gauge-covariant kinematical momentum operator (velocity ...
Interacting electrons in a 2D quantum dot Akman, N; Tomak, Mehmet (1999-04-01) The exact numerical diagonalization of the Hamiltonian of a 2D circular quantum dot is performed for 2, 3, and 4 electrons. The results an compared with those of the perturbation theory. Our numerical results agree reasonably well for small values of the dimensionless coupling constant lambda = a/a(B) where a is the dot radius and a(B) is the effective Bohr radius. Exact diagonalization results are compared with the classical predictions, and they are found to be almost coincident for large lambda values.
HAMILTONIAN QUANTIZATION OF THE CP1 SIGMA MODEL IN 1+2 DIMENSIONS Pak, Namık Kemal (1992-09-01) CP1 sigma model with Hopf interaction in 1 + 2 dimensions is quantized canonically using a lifted formulation. In this formulation the Hopf invariant is still a local functional of the fields. However, the constraint structure is as simple as that of a U(1) gauge theory without any nonlinearity constraints. As a by-product, the theta-dependent fractional spin is computed in this local setting.

Citation Formats

M. S. Shikakhwa, “Spin force and torque in non-relativistic Dirac oscillator on a sphere,” PHYSICS LETTERS A, pp. 855–859, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63938.