We determine the largest rate of exponential decay at infinity for non-trivial solutions to the Dirac equation $${{𝒟}}_n\psi +𝕍\psi =0\text{in }{ℝ}^n,$$ being ${{𝒟}}_n$ the massless Dirac operator in dimension $n\ge 2$ and $𝕍$ a (possibly non-Hermitian) matrix-valued perturbation such that $|𝕍(x)|\sim |x{|}^{-𝜖}$ at infinity, for $-\infty <𝜖<1$. Also, we show that our results are sharp for $n\in \{2,3\}$, providing explicit examples of solutions that have the prescripted decay, in presence of a potential with the related behavior at infinity. As a consequence, we investigate the exponential decay at infinity for the eigenfunctions of the perturbed massive Dirac operator, and determine the sharpest possible decay in the case that $𝜖\le 0$ and $n\in \{2,3\}$.

我们确定Dirac方程的非平凡解的无穷大最大指数衰减率 $${{𝒟}}_{ñ}\psi +𝕍\psi =0\text{在 }{ℝ}^{ñ}，$$ 存在 ${{𝒟}}_{ñ}$ 维度上无质量的Dirac算子 $ñ\ge 2$ 和 $𝕍$ 一个（可能是非Hermitian的）矩阵值摄动，使得 $|𝕍（X）|〜|X{|}^{-𝜖}$ 在无限远时 $-\infty <𝜖<\mathrm{1个}$。此外，我们证明了我们的结果对于$ñ\in \{2，3\}$，提供了具有规定衰减的解决方案的显式示例，其中存在具有无穷大相关行为的电势。结果，我们研究了被摄动的大规模狄拉克算子的本征函数在无穷大处的指数衰减，并在以下情况下确定了最尖锐的衰减：$𝜖\le 0$ 和 $ñ\in \{2，3\}$。