Complete kinematic null for local kinetic dissipation in a sixfold-driven electron fluid

Abstract

We identify a complete kinematic null in a two-dimensional electron fluid driven by a sixfold boundary pattern. In the $U_3^{\pm }$ channel of $D_{12}$, device symmetry excludes both the vector representation $R_1$ and the full first-gradient tensor $R_1\otimes R_1$. Hence at the symmetry-fixed center $\mathbf{j}(0)=0$ and ${\partial }_i{j}_j(0)=0$, so every local quadratic dissipative form built from the modeled charge/momentum field through first gradient order vanishes independently of the constitutive coefficients. In an $O(2)$-isotropic angular-harmonic kinetic model the first allowed local sector is $m=3$. For $\nu q^2/{\gamma }_3\ll 1$, its heating is set by the previously derived coefficient ${\kappa }_4=v_F^4/(16{\gamma }_2^2{\gamma }_3)$. An explicit incompressible Stokes disk realizes a nonzero center signal, and a finite-moment kinetic boundary-value solution approaches the corresponding local benchmark. Within the local, fixed-current momentum-conserving Stokes regime, the normalized magnetic response can then be fitted for effective ${\gamma }_3$ and ${\gamma }_2$. Thus the sixfold drive creates a measurement point where ordinary local charge/momentum hydrodynamic dissipation is absent while a kinetic mode remains finite.

13 pages total; 3 main-text figures; Supplemental Material included in the same PDF