This paper studies localization transitions in non-Hermitian quantum mechanics, focusing on one- and two-dimensional systems with random Schrödinger equations under a constant imaginary vector potential. The authors relate this to flux line depinning in superconductors under a transverse magnetic field, predicting stretched exponential relaxation and diverging penetration depth at the transition. Non-Hermitian Hamiltonians, though forbidden in conventional quantum mechanics, appear in classical statistical mechanics and describe nonequilibrium processes. The study maps flux lines in superconductors to boson world lines, with columnar defects introducing random potentials. The paper shows that flux lines can be depinned from defects by a strong perpendicular magnetic field, indicating extended states in a large $ H_{\perp} $ region and a delocalization transition. The non-Hermitian Hamiltonian has the form $ \mathcal{H} \equiv (\pmb{p} + i\hbar)^{2}/(2m) + V(\pmb{x}) $, with $ \pmb{p} \equiv (\hbar/i)\nabla $ and $ V(\pmb{x}) $ a random potential. The imaginary part of the current describes the tilt slope of a flux line. The paper investigates localized and delocalized states, showing that the delocalization transition occurs when $ |h| = \hbar\kappa $. For a single attractive impurity, the ground state is localized for $ h < \hbar \kappa_{gs} $, and becomes extended for $ h > \hbar \kappa_{gs} $. In the random potential case, the non-Hermitian tight-binding model is used, with complex eigenvalues appearing in conjugate pairs. The paper also discusses the behavior of flux lines in two dimensions, showing that delocalized states can extend in both directions parallel and perpendicular to $ h $. The study concludes that the delocalization transition is characterized by a diverging penetration depth and stretched exponential relaxation, with the flux line's tilt slope changing at the transition. The paper also discusses the behavior of flux lines near free surfaces and the relaxation of flux lines from the surface to occupied states. The results are relevant for understanding the behavior of interacting flux lines at low but finite concentrations.This paper studies localization transitions in non-Hermitian quantum mechanics, focusing on one- and two-dimensional systems with random Schrödinger equations under a constant imaginary vector potential. The authors relate this to flux line depinning in superconductors under a transverse magnetic field, predicting stretched exponential relaxation and diverging penetration depth at the transition. Non-Hermitian Hamiltonians, though forbidden in conventional quantum mechanics, appear in classical statistical mechanics and describe nonequilibrium processes. The study maps flux lines in superconductors to boson world lines, with columnar defects introducing random potentials. The paper shows that flux lines can be depinned from defects by a strong perpendicular magnetic field, indicating extended states in a large $ H_{\perp} $ region and a delocalization transition. The non-Hermitian Hamiltonian has the form $ \mathcal{H} \equiv (\pmb{p} + i\hbar)^{2}/(2m) + V(\pmb{x}) $, with $ \pmb{p} \equiv (\hbar/i)\nabla $ and $ V(\pmb{x}) $ a random potential. The imaginary part of the current describes the tilt slope of a flux line. The paper investigates localized and delocalized states, showing that the delocalization transition occurs when $ |h| = \hbar\kappa $. For a single attractive impurity, the ground state is localized for $ h < \hbar \kappa_{gs} $, and becomes extended for $ h > \hbar \kappa_{gs} $. In the random potential case, the non-Hermitian tight-binding model is used, with complex eigenvalues appearing in conjugate pairs. The paper also discusses the behavior of flux lines in two dimensions, showing that delocalized states can extend in both directions parallel and perpendicular to $ h $. The study concludes that the delocalization transition is characterized by a diverging penetration depth and stretched exponential relaxation, with the flux line's tilt slope changing at the transition. The paper also discusses the behavior of flux lines near free surfaces and the relaxation of flux lines from the surface to occupied states. The results are relevant for understanding the behavior of interacting flux lines at low but finite concentrations.