Abstract
We consider the dynamics of Dirac particles moving in the curved spaces of variable dimension interpolating smoothly between 3- and 2-dimensional spaces and considered as a toy model for 2-dimensional structures in solid state physics. Performing the Foldy-Wouthuysen (FW) transformation of Dirac equation and passing to the classical limit, we derive the equations of motion of momentum and spin. The spin precesses with the variable angular velocity and may "flick" appearing in the remnant 2-dimensional space twice during the period.
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