Propagator for a charged anisotropic oscillator in a constant magnetic field

Kokiantonis, N.; Castrigiano, K

doi:10.1088/0305-4470/18/1/015

Cited by 20 publications

(6 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The corresponding cases in flat space are well-known, e.g. [31,32,58,74]. A systematic study for the search of separable potentials in IR 2 and IR 3 does exist [26,30], a project which has been started by Smorodinsky, Winternitz et al [81].…”

Section: Discussion and Summarymentioning

confidence: 99%

Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions

Grosche

1994

Fortschr. Phys.

View full text Add to dashboard Cite

In this paper path integration in two‐ and three‐dimensional spaces of constant curvature is discussed: i.e. the flat spaces R2 and R3, the two‐ and three‐dimensional sphere and the two‐ and three‐dimensional pseudosphere. We are going to discuss all coordinates systems where the Laplace operator admits separation of variables. In all of them the path integral formulation will be stated, however in most of them an explicit solution in terms of the spectral expansion can be given only on a formal level. What can be stated in all cases, are the propagator and the corresponding Green function, respectively, depending on the invariant distance which is a coordinate independent quantity. This property gives rise to numerous identities connecting the corresponding path integral representations and propagators in various coordinate systems with each other.

show abstract

Section: Discussion and Summarymentioning

confidence: 99%

Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions

Grosche

1994

Fortschr. Phys.

View full text Add to dashboard Cite

show abstract

“…In contrast, there exist quite a lot of studies for the anisotropic QDs where the broken rotational symmetry brings in lots of new physics, especially the effects of anisotropy. [30][31][32][33][34][35][36][37][38][39][40][41][42] For instance, the shell structure pattern in the addition energy spectra is much less pronounced for small deformations and vanishes for stronger anisotropies. [31] The degeneracy in the single-particle excitation spectrum is lifted due to the reduction of the symmetry and the selection rules are affected by producing coupling effects between the states.…”

Section: Introductionmentioning

confidence: 99%

Magnetpolaron effect in two-dimensional anisotropic parabolic quantum dot in a perpendicular magnetic field

Ju¹,

Guo²,

Pan³

2017

Chinese Phys. B

View full text Add to dashboard Cite

We study the two-dimensional weak-coupling Fröhlich polaron in a completely anisotropic quantum dot in a perpendicular magnetic field. By performing a unitary transformation, we first transform the Hamiltonian into a new one which describes an anisotropic harmonic oscillator with new mass and trapping frequencies interacting with the same phonon bath but with different interaction form and strength. Then employing the second-order Rayleigh-Schrödinger perturbation theory, we obtain the polaron correction to the ground-state energy. The magnetic field and anisotropic effects on the polaron correction to the ground-state energy are discussed.

show abstract

“…The anisotropic case with a homogeneous static magnetic field was studied in Refs. [5] and [6]. In these works the magnetic field was arranged to point to one of the rectangular axis directions.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Harmonic Oscillator in a Static Electromagnetic Field

Lin¹

2002

Commun. Theor. Phys.

View full text Add to dashboard Cite

A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrödinger equation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. In some of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherent and squeezed states and their time evolution are discussed in detail.

show abstract

Propagator for a charged anisotropic oscillator in a constant magnetic field

Cited by 20 publications

References 2 publications

Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions

Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions

Magnetpolaron effect in two-dimensional anisotropic parabolic quantum dot in a perpendicular magnetic field

Anisotropic Harmonic Oscillator in a Static Electromagnetic Field

Contact Info

Product

Resources

About