Real-Time Simulation of Asymmetry Generation in Fermion-Bubble Collisions

Motivated by the out-of-equilibrium dynamics during an early-universe first-order phase transition, we perform real-time simulations of fermion-bubble scattering in $1+1$ dimensions. This nonequilibrium process can generate a charge-conjugation $\mathsf{C}$ asymmetry outside the bubble wall, induced by the complex fermion mass profile. The resulting $\mathsf{C}$ asymmetry is the 1+1-dimensional analog of the $\mathsf{CP}$ asymmetry in 3+1 dimensions, a key ingredient in baryon asymmetry generation at the electroweak scale. Using tensor network methods, we track the real-time evolution of the $\mathsf{C}$ asymmetry in the charge density as the fermion interacts with the bubble wall, a regime inaccessible to analytic calculations. We further introduce two observables to quantify the asymmetry in the asymptotic region where reflected particles are well separated from the scattering point: one based on the net charge outside the bubble wall, and the other on the spatial displacement between the reflected particle and antiparticle wavepackets. Our study represents a first step toward nonperturbative, real-time computations of $\mathsf{CP}$ asymmetry in 3+1 dimensions for electroweak baryogenesis.