Multiple Time Stepping Methods for Numerical Simulation of Charge Transfer by Mobile Discrete Breathers

Abstract

In this work we propose new structure-preserving multiple time stepping methods for numerical simulation of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by classical Hamiltonian dynamics, whereas charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Proposed multiple time stepping schemes are based on symplecticity-preserving symmetric splitting methods recently developed by the authors. Originally developed explicit splitting methods do not exactly conserve total charge probability, thus, to improve charge probability conservation and to better resolve high frequency oscillations of the charge in numerical simulations with large time steps we incorporate multiple time stepping approach when solving split charge equations. Improved numerical results with multiple time stepping methods of charge transfer by mobile discrete breathers are demonstrated in a crystal lattice model example.