- -

High order efficient splittings for the semiclassical time-dependent Schrodinger equation

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

High order efficient splittings for the semiclassical time-dependent Schrodinger equation

Mostrar el registro completo del ítem

Blanes Zamora, S.; Gradinaru, V. (2020). High order efficient splittings for the semiclassical time-dependent Schrodinger equation. Journal of Computational Physics. 405:1-13. https://doi.org/10.1016/j.jcp.2019.109157

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/163757

Ficheros en el ítem

Thumbnail
Nombre: Blanes;Gradinaru - ...
Tamaño: 580.1Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir/Preview
[Cerrado]
Nombre: 2020_JComputPhys.pdf
Tamaño: 861.5Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor

Metadatos del ítem

Título: High order efficient splittings for the semiclassical time-dependent Schrodinger equation
Autor: Blanes Zamora, Sergio Gradinaru, Vasile
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[EN] Standard numerical schemes with time-step h deteriorate (e.g. like epsilon(-2)h(2)) in the presence of a small semiclassical parameters in the time-dependent Schrodinger equation. The recently introduced semiclassical ...[+]
Palabras clave: Semiclassical , Time-dependent Schrodinger equation , Splitting , Wavepackets
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Journal of Computational Physics. (issn: 0021-9991 )
DOI: 10.1016/j.jcp.2019.109157
Editorial:
Elsevier
Versión del editor: https://doi.org/10.1016/j.jcp.2019.109157
Código del Proyecto:
info:eu-repo/grantAgreement/MINECO//MTM2016-77660-P/ES/NUEVOS RETOS EN INTEGRACION NUMERICA: FUNDAMENTOS ALGEBRAICOS, METODOS DE ESCISION, METODOS DE MONTECARLO Y OTRAS APLICACIONES/
Agradecimientos:
The work of SB has been funded by Ministerio de Economia, Industria y Competitividad (Spain) through project MTM2016-77660-P (AEI/FEDER, UE).
Tipo: Artículo

References

Bao, W., Jin, S., & Markowich, P. A. (2002). On Time-Splitting Spectral Approximations for the Schrödinger Equation in the Semiclassical Regime. Journal of Computational Physics, 175(2), 487-524. doi:10.1006/jcph.2001.6956

Balakrishnan, N., Kalyanaraman, C., & Sathyamurthy, N. (1997). Time-dependent quantum mechanical approach to reactive scattering and related processes. Physics Reports, 280(2), 79-144. doi:10.1016/s0370-1573(96)00025-7

Descombes, S., & Thalhammer, M. (2010). An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime. BIT Numerical Mathematics, 50(4), 729-749. doi:10.1007/s10543-010-0282-4 [+]
Bao, W., Jin, S., & Markowich, P. A. (2002). On Time-Splitting Spectral Approximations for the Schrödinger Equation in the Semiclassical Regime. Journal of Computational Physics, 175(2), 487-524. doi:10.1006/jcph.2001.6956

Balakrishnan, N., Kalyanaraman, C., & Sathyamurthy, N. (1997). Time-dependent quantum mechanical approach to reactive scattering and related processes. Physics Reports, 280(2), 79-144. doi:10.1016/s0370-1573(96)00025-7

Descombes, S., & Thalhammer, M. (2010). An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime. BIT Numerical Mathematics, 50(4), 729-749. doi:10.1007/s10543-010-0282-4

Bader, P., Iserles, A., Kropielnicka, K., & Singh, P. (2014). Effective Approximation for the Semiclassical Schrödinger Equation. Foundations of Computational Mathematics, 14(4), 689-720. doi:10.1007/s10208-013-9182-8

Gradinaru, V., & Hagedorn, G. A. (2013). Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation. Numerische Mathematik, 126(1), 53-73. doi:10.1007/s00211-013-0560-6

Keller, J., & Lasser, C. (2013). Propagation of Quantum Expectations with Husimi Functions. SIAM Journal on Applied Mathematics, 73(4), 1557-1581. doi:10.1137/120889186

Gradinaru, V., Hagedorn, G. A., & Joye, A. (2010). Tunneling dynamics and spawning with adaptive semiclassical wave packets. The Journal of Chemical Physics, 132(18), 184108. doi:10.1063/1.3429607

Gradinaru, V., Hagedorn, G. A., & Joye, A. (2010). Exponentially accurate semiclassical tunneling wavefunctions in one dimension. Journal of Physics A: Mathematical and Theoretical, 43(47), 474026. doi:10.1088/1751-8113/43/47/474026

Coronado, E. A., Batista, V. S., & Miller, W. H. (2000). Nonadiabatic photodissociation dynamics ofICNin the à continuum: A semiclassical initial value representation study. The Journal of Chemical Physics, 112(13), 5566-5575. doi:10.1063/1.481130

Church, M. S., Hele, T. J. H., Ezra, G. S., & Ananth, N. (2018). Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation. The Journal of Chemical Physics, 148(10), 102326. doi:10.1063/1.5005557

Hagedorn, G. A. (1998). Raising and Lowering Operators for Semiclassical Wave Packets. Annals of Physics, 269(1), 77-104. doi:10.1006/aphy.1998.5843

Faou, E., Gradinaru, V., & Lubich, C. (2009). Computing Semiclassical Quantum Dynamics with Hagedorn Wavepackets. SIAM Journal on Scientific Computing, 31(4), 3027-3041. doi:10.1137/080729724

McLachlan, R. I. (1995). Composition methods in the presence of small parameters. BIT Numerical Mathematics, 35(2), 258-268. doi:10.1007/bf01737165

Blanes, S., Casas, F., & Ros, J. (1999). Symplectic Integration with Processing: A General Study. SIAM Journal on Scientific Computing, 21(2), 711-727. doi:10.1137/s1064827598332497

Blanes, S., Casas, F., & Ros, J. (2000). Celestial Mechanics and Dynamical Astronomy, 77(1), 17-36. doi:10.1023/a:1008311025472

Blanes, S., Diele, F., Marangi, C., & Ragni, S. (2010). Splitting and composition methods for explicit time dependence in separable dynamical systems. Journal of Computational and Applied Mathematics, 235(3), 646-659. doi:10.1016/j.cam.2010.06.018

Stefanov, B., Iordanov, O., & Zarkova, L. (1982). Interaction potential in1Σg+Hg2: fit to the experimental data. Journal of Physics B: Atomic and Molecular Physics, 15(2), 239-247. doi:10.1088/0022-3700/15/2/010

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem