Exact spectrum of the two-dimensional rigid rotator in external fields. II. Zeeman effect

1981 ◽  
Vol 24 (1) ◽  
pp. 342-344 ◽  
Author(s):  
Mark P. Silverman
Keyword(s):  
Zeeman Effect ◽  
Two Dimensional ◽  
External Fields ◽  
Rigid Rotator

scholarly journals Nematic topological defects positionally controlled by geometry and external fields

2018 ◽  
Vol 9 ◽  
pp. 109-118 ◽  
Author(s):  
Pavlo Kurioz ◽  
Marko Kralj ◽  
Bryce S Murray ◽  
Charles Rosenblatt ◽  
Samo Kralj
Keyword(s):  
Electric Field ◽  
Topological Charge ◽  
Order Parameter ◽  
Topological Defects ◽  
Two Dimensional ◽  
External Fields ◽  
Nematic Ordering ◽  
Spatial Positioning ◽  
A Charge ◽  
The Impact

Using a Landau–de Gennes approach, we study the impact of confinement topology, geometry and external fields on the spatial positioning of nematic topological defects (TDs). In quasi two-dimensional systems we demonstrate that a confinement-enforced total topological charge of m > 1/2 decays into elementary TDs bearing a charge of m = 1/2. These assemble close to the bounding substrate to enable essentially bulk-like uniform nematic ordering in the central part of a system. This effect is reminiscent of the Faraday cavity phenomenon in electrostatics. We observe that in certain confinement geometries, varying the correlation length size of the order parameter could trigger a global rotation of an assembly of TDs. Finally, we show that an external electric field could be used to drag the boojum fingertip towards the interior of the confinement cell. Assemblies of TDs could be exploited as traps for appropriate nanoparticles, opening several opportunities for the development of functional nanodevices.

scholarly journals Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

2017 ◽  
Vol 76 ◽  
pp. 1-11 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Bound States ◽  
Diatomic Molecules ◽  
Zeeman Effect ◽  
Real Space ◽  
Group Symmetry ◽  
Dimensional System ◽  
Two Dimensional ◽  
Spin Orbital ◽  
Space Phase ◽  
Type Potential

In this work, an analytical expression for the nonrelativistic energy spectrum of some diatomic molecules was obtained through the Bopp’s shift method in the noncommutative (NC) two-dimensional real space-phase symmetries (NC: 2D-RSP) with a new modified Kratzer-type potential (NMKP) in the framework of two infinitesimal parameters and due to (space-phase) noncommutativity, by means of the solution of the noncommutative Schrödinger equation. The perturbation property of the spin-orbital Hamiltonian operator and new Zeeman effect of two-dimensional system are investigated. We have shown that, the new energy of diatomic molecule is the sum of ordinary energy of modified Kratzer-type potential, in commutative space, and new additive terms due to the contribution of the additive part of the NMKP. We have shown also that, the group symmetry of (NC: 2D-RSP) reduce to new sub-group symmetry of NC two-dimensional real space (NC: 2D-RSP) under new modified Kratzer-type interactions.

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