Infinitesimal Rotations and Constraints in Physics

U. Fano, A. R. P. Rau

Karmela Padavić, Kuei Sun, Courtney Lannert +1 more

Shell-shaped hollow Bose-Einstein condensates (BECs) exhibit behavior distinct from their filled counterparts and have recently attracted attention due to their potential realization in microgravity settings. Here we study distinct features of these hollow structures stemming from vortex physics and the presence of rotation. We focus on a vortex-antivortex pair as the simplest configuration allowed by the constraints on superfluid flow imposed by the closed-surface topology. In the two-dimensional limit of an infinitesimally thin shell BEC, we characterize the long-range attraction between the vortex-antivortex pair and find the critical rotation speed that stabilizes the pair against energetically relaxing towards self-annihilation. In the three-dimensional case, we contrast the bounds on vortex stability with those in the two-dimensional limit and the filled sphere BEC, and evaluate the critical rotation speed as a function of shell thickness. We thus demonstrate that analyzing vortex stabilization provides a nondestructive means of characterizing a hollow sphere BEC and distinguishing it from its filled counterpart.

Thomas A. Brody

Hà ⁄ seyin Önal

It is shown that Pauli Matrixes can be derived from irreducible rotation group representations of the weight =1/2, which in turn based on the system of infinitesimal (elementary) spatial rotations. The last permits to substantiate why Pauli matrixes can be so sufficiently used for modeling of physical rotations.

Paul Chambadal

Hüseyin Önal

It is shown that Pauli Matrixes can be derived from irreducible rotation group representations of the weight =1/2, which in turn based on the system of infinitesimal (elementary) spatial rotations. The last permits to substantiate why Pauli matrixes can be so sufficiently used for modeling of physical rotations.