O. I. Tolstikhin | Searcharxiv

arXiv2023

Integral representations for products of two solutions of the Airy equation with shifted arguments and their applications in physics

Integral representations for a complete set of linearly independent products of two solutions of the Airy equation whose arguments differ by $z_0$ are obtained using the Laplace contour integral method. This generalizes similar integral representations for the case $z_0=0$ obtained by Reid. The relation to other previous results is discussed. The results are used to obtain the outgoing-wave Green's function for an electron in a static electric field in a closed analytic form.

quant-ph↗

arXiv2006

Vortex creation during magnetic trap manipulations of spinor Bose-Einstein condensates

We investigate several mechanisms of vortex creation during splitting of a spinor BEC in a magnetic trap controlled by a pair of current carrying wires and bias magnetic fields. Our study is motivated by a recent MIT experiment on splitting BECs with a similar trap, where unexpected fork-like structure appeared in the interference fringes corresponding to interference of two condensates, one with and the other without a singly quantized vortex. It is well-known that in a spin-1 BEC in a quadrupole trap a doubly quantized vortex is produced topologically by a ``slow'' reversal of bias magnetic field $B_z$. We find that in the magnetic trap considered it is also possible to produce a 4- and 1-quantized vortex in a spin-1 BEC. The latter is possible, for example, during the magnetic field switching-off process. We therefore provide a possible explanation for the unexpected interference patterns in the experiment. We also give an example of the creation of singly quantized vortices due to ``fast'' splitting, which is a possible alternative mechanism of the interference pattern.

cond-mat.other↗