Artículo
Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
Autor/es | Bajārs, Jānis
Archilla, Juan F. R. |
Departamento | Universidad de Sevilla. Departamento de Física Aplicada I |
Fecha de publicación | 2022-09-22 |
Fecha de depósito | 2023-04-17 |
Publicado en |
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Resumen | We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without ... We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics 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 the charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Canonical Hamiltonian equations for coupled lattice-charge dynamics are derived, and a linear analysis of linearized equations with the derivation of the dispersion relations is performed. Structure-preserving splitting methods are constructed by splitting the total Hamiltonian into the sum of Hamiltonians, for which the individual dynamics can be solved exactly. Symmetric methods are obtained with the Strang splitting of exact, symplectic flow maps leading to explicit second-order numerical integrators. Splitting methods that are symplectic and conserve exactly the charge probability are also proposed. Conveniently, they require only one solution of a linear system of equations per time step. The developed methods are computationally efficient and preserve the structure; therefore, they provide new means for qualitative numerical analysis and long-time simulations for charge transfer by nonlinear lattice excitations. The properties of the developed methods are explored and demonstrated numerically considering charge transport by mobile discrete breathers in an example model previously proposed for a layered crystal |
Agencias financiadoras | Ministerio de Ciencia, Innovación y Universidades (MICINN). España Junta de Andalucía |
Identificador del proyecto | PID2019-109175GB-C22
US-1380977 |
Cita | Bajārs, J. y Archilla, J.F.R. (2022). Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices. Mathematics, 10 (19). https://doi.org/10.3390/math10193460. |
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