Infrared Memory and Scrambling in a Dynamically Opened Coupled-SYK Majorana Junction

Abstract: We study a dynamically opened Majorana junction formed by two coupled Sachdev--Ye--Kitaev (SYK) systems. A time-dependent bilinear coupling drives the system from a nearly decoupled to a strongly hybridized regime, providing an interacting realization of a Majorana shutter. Using a low-frequency analysis of the large-$N$ Keldysh theory around the conformal $q=4$ SYK saddle, we find that the opening retains a strong infrared memory, with the associated anomalous response becoming increasingly sensitive to the infrared cutoff. Exact finite-dimensional simulations of two $N=8$ SYK clusters show enhanced inter-sector entanglement, parity transfer, and cross-sector operator scrambling after the opening. These results connect the infrared structure of conformal SYK dynamics with finite-size many-body scrambling and show how a dynamically opened interacting Majorana system can retain long-wavelength memory beyond the quadratic limit.