Inertial spin Hall effect in noncommutative space

TL;DR

This paper investigates how noncommutative space modifies the inertial spin Hall effect, deriving explicit $ heta$-dependent corrections and proposing experimental bounds on the noncommutative parameter through observable spin polarization.

Contribution

It extends the inertial spin current analysis to noncommutative space and derives explicit $ heta$-dependent corrections, providing a new experimental approach to measure noncommutativity.

Findings

Derived $ heta$-dependent corrections to inertial spin current and conductivity.

Established bounds on the noncommutative parameter $ heta$ from observable spin polarization.

Demonstrated the non-trivial effects of noncommutativity on the Hamiltonian in an accelerating frame.

Abstract

In the present paper the study of inertial spin current(that appears in an accelerated frame of reference) is extended to Non-Commutative (NC) space. The $\theta$-dependence, ($\theta$ being the NC parameter), of the inertial spin current is derived explicitly. We have provided yet another way of experimentally measuring $\theta$. Our bound on $\theta$ matches with previous results. In Hamiltonian framework, the Dirac Hamiltonian in an accelerating frame is computed in the low energy regime by exploiting the Foldy-Wouthuysen scheme. The NC $\theta$-effect appears from the replacement of normal products and commutators by Moyal *-products and *-commutators. In particular, the commutator between the external magnetic vector potential and the potential induced by acceleration becomes non-trivial. Expressions for $\theta$-corrected inertial spin current and conductivity are derived. The $\theta$ bound is obtained from the out of plane spin polarization, which is experimentally observable.