Discontinuous quenching of quasi-particle states in nonequilibrium dynamical mean-field theory

In an effort to model strongly correlated heterojunctions in nonequilibrium we construct a nonequilibrium dynamical mean-field theory for the Hubbard model where each lattice site is a superposition of a left-moving and right-moving state. The left and right movers have the respective chemical potentials, $\mu_L=\frac{\Phi}{2}$ and $\mu_R=-\frac{\Phi}{2}$, where $\Phi$ is the chemical potential bias. The quasi- particle properties are calculated as a function of the Coulomb interaction, $U$, and $\Phi$. As the chemical potential bias is turned on we find that the quasi-particles become strongly renormalized. When $U_d