Abstract

In this paper, we derive new results on the asymptotic behavior of eigenvalues of perturbed one-dimensional massive Dirac operators in the weak coupling limit. Two classes of potentials are considered. For bounded Hermitian potentials V satisfying |V(x)|less than or similar to|x|-1 for large |x|, we recover the leading term, which may include a logarithmic correction if V(x)similar to|x|-1 at infinity. For possibly non-Hermitian L1 potentials satisfying a suitable moment condition, we obtain the second term in the asymptotic expansion. The first result is based on a min-max principle adapted to the nonrelativistic limit, while the second result is obtained via the Birman-Schwinger principle and resolvent expansions.