In the holographic model of Dirac semimetals, the Einstein–Maxwell scalar gravity with the auxiliary U(1)-gauge field, coupled to the ordinary Maxwell one by a kinetic mixing term, the black brane response to the electric fields and temperature gradient has been elaborated. Using the foliation by hypersurfaces of constant radial coordinate we derive the exact form of the Hamiltonian and equations of motion in the phase space considered. Examination of the Hamiltonian constraints enables us, to the leading order expansion of the linearised perturbations at the black brane event horizon, to derive the Stokes equations for an incompressible doubly charged fluid. Solving the aforementioned equations, one arrives at the DC conductivities for the holographic Dirac semimetals.

在狄拉克半金属的全息模型中，爱因斯坦-麦克斯韦标量引力与辅助U（1）标量场通过动力学混合项耦合到普通麦克斯韦之一，对电场和温度梯度的黑糠响应为详细说明。使用恒定径向坐标的超曲面的叶面化，我们得出了哈密顿量的精确形式和所考虑的相空间中的运动方程。哈密​​顿约束的检验使我们能够对黑糠事件水平线上的线性扰动进行前导展开，从而导出不可压缩的双电荷流体的斯托克斯方程。通过求解上述方程，可以得出全息狄拉克半金属的直流电导率。