Infrared Memory of a Majorana Shutter

Abstract

We study a finite-width Majorana shutter as a local, time-dependent scattering defect and determine which features of its infrared memory are insensitive to the microscopic spatial profile. For a smooth shutter, the zero-frequency scattering matrix is fixed by the integrated coupling, while finite-width corrections vanish in the long-wavelength limit. A time-dependent switch then produces an infrared Bogoliubov kernel whose singular part is controlled by the change in this scattering matrix. We examine the many-body response through three observables. The overlap of the pre- and post-shutter Gaussian vacua exhibits Anderson orthogonality, with an exponent set by the scattering angle. A lattice calculation of the post-quench quasiparticle number resolves its logarithmic infrared growth, reaching the predicted coefficient in the slow-switch test and reproducing the expected dependence on the scattering-angle change. When the entanglement cut passes through the shutter, the entropy follows the effective-central-charge description of a conformal defect, with parameter-free agreement at the percent level, improving for the wider shutter. When the shutter lies inside the interval, its contribution remains a subleading finite-size correction. A local bilinear correlator approaches the expected Majorana power law and shows no stable logarithmic amplitude. These results show that the same low-frequency scattering data control distinct global and spatial observables, while their infrared coefficients are not interchangeable. The remaining limits are also made explicit: the finite-memory correction to the continuum kernel and the controlled continuum limit of large-interval spatial entropy.