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Notes on the Krupa-Zawisza ultrapower of self-adjoint operators

Ando H., Saigo H., Ojima I.

Probability and Mathematical Statistics

2014

Vol. 34, Fasc. 1

147--159

Let ω ∈ βN \ N be a free ultrafilter on N. It is known that there is a difficulty in constructing the ultrapower of unbounded operators. Krupa and Zawisza gave a rigorous definition of the ultrapower Aω of a self-adjoint operator A. In this note, we give an alternative description of Aω and the Hilbert space H(A) on which Aω is densely defined. This provides a criterion to determine a representing sequence (ξn)n of a given vector ξ ∈ dom(Aω) which has the property that Aωξ = (Aξn)ω holds. An explicit core for Aω is also described.

Overhauser effect and anisotropy of electron spin g-factor in GaAs / AlGaAs quantum wells

Ito T., Shichi W., Ichida M., Gotoh H., Kamada H., Ando H.

Journal of Automation Mobile Robotics and Intelligent Systems

2009

Vol. 3, No. 4

105-107

To investigate the dependence of electron g-factor on magnetic field in GaAs / AlGaAs quantum wells time-resolved photoluminescence measurements under a high magnetic field in different experimental configuration, the magnetic field perpendicular (g up tack ) and parallel (g II) to the quantum confinement direction, has been studied. When the angle between the magnetic field and the confinement direction is 45°, the precession frequency varies depending on polarity of magnetic field and the circular polarization type of excitation light (sigma+ or sigma-). We found that these dependences of the precession frequency exhibit main features of Overhauser effect with an effective magnetic field of 0.5 T that nuclear spins react back on electron spin precession and the g-factor value is not affected by the effective magnetic field. The g+ and gii values agree well with the results of four-band k • p perturbation calculations.