Quantum statistical theory of dislocation mobility in discrete lattices

We present a first-principles quantum statistical theory of dislocation motion based on discrete lattice dynamics and the Keldysh nonequilibrium formalism. By treating the dislocation as a moving source coupled to the phonon field through exact Kanzaki forces, we derive a universal memory kernel that captures all phononmediated dissipation mechanisms without adjustable parameters. The theory naturally produces the experimentally observed drag regimes: linear phonon wind at low velocities, quadratic radiation damping at intermediate speeds, and finite drag enhancement near the speed of sound. Crucially, we demonstrate that the elastodynamic prediction of an infinite sound barrier is an artefact of continuum approximations; the discrete lattice structure and anharmonic phonon interactions regularize all singularities, permitting transonic motion at finite stress. Through systematic reduction via conserving approximations, we obtain practical mobility laws suitable for crystal plasticity and dislocation dynamics simulations. These take the form of either steady state algebraic relations or minimal differential systems that capture memory effects while adding negligible computational cost. All parameters derive directly from harmonic and anharmonic force constants, enabling predictive modeling across ten orders of magnitude in strain rate. Application to fcc and bcc metals yields drag coefficients and relaxation times in good agreement with molecular dynamics and available experiments, validating the approach. This work establishes a microscopic foundation for dislocation mobility and provides a pathway from atomistic properties to continuum plasticity without empirical fitting.