Spectral analysis for the almost periodic quadratic pencil with impulse

In this study, we delve into the spectral properties of a pencil of nonself-adjoint second-order differential operators characterized by almost periodic potentials and impulse conditions. Such operators arise in various physical models, particularly in quantum mechanics, where they describe systems with discontinuities in their potentials or boundary conditions. Understanding the spectrum of these operators is crucial for comprehending the stability and dynamics of the associated physical systems. By investigating the spectral gaps and accumulation points we aim to contribute to the broader understanding of non-self-adjoint operator theory and its applications in mathematical physics.