835 research outputs found
Unimodality for free multiplicative convolution with free normal distributions on the unit circle
We study unimodality for free multiplicative convolution with free normal
distributions on the unit circle. We give four results on
unimodality for : (1) if is a symmetric unimodal
distribution on the unit circle then so is at any time
; (2) if is a symmetric distribution on supported on
for some , then is unimodal for sufficiently large
; (3) is not unimodal at any time ,
where is the equally weighted Bernoulli distribution on ;
(4) is not freely strongly unimodal for sufficiently small .
Moreover, we study unimodality for classical multiplicative convolution (with
Poisson kernels), which is useful in proving the above four results.Comment: 19 pages, 4 figure
Can Spinor Dipolar Effects be Observed in Bose-Einstein Condensates?
Weak dipolar effects in atomic Bose-Einstein condensates (BECs) have recently
been predicted to develop spin textures. However, observation of these effects
requires magnetic field as low as G for spin-1 alkali BECs, so
that they are not washed out by the Zeeman effect. We present a scheme to
observe the magnetic dipole-dipole interaction in alkali BECs under a realistic
magnetic field of mG. Our scheme enables us to extract genuine
dipolar effects and should apply also to Cr BECs.Comment: 4 pages, 3 figure
Breaking of Chiral Symmetry and Spontaneous Rotation in a Spinor Bose-Einstein Condensate
We show that a spin-1 Bose-Einstein condensate with ferromagnetic
interactions spontaneously generates a topological spin texture, in which the m
= \pm 1 components of the magnetic sublevels form vortices with opposite
circulations. This phenomenon originates from an interplay between
ferromagnetic interactions and spin conservation.Comment: 5 pages, 4 figure
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