Bader, P.; Blanes Zamora, S.; Casas, F. (2013). Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex coefficients. Journal of Chemical Physics. 139(12):124117-124117. doi:10.1063/1.4821126
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/44813
Title:
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Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex coefficients
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Author:
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Bader, Philipp
Blanes Zamora, Sergio
Casas, Fernando
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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The Schrodinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional ...[+]
The Schrodinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional time steps of order greater than two necessarily have negative steps and cannot be used for this class of diffusive problems. However, there exist methods which use fractional complex time steps with positive real parts which can be used with only a moderate increase in the computational cost. We analyze the performance of this class of schemes and propose new methods which outperform the existing ones in most cases. On the other hand, if the gradient of the potential is available, methods up to fourth order with real and positive coefficients exist. We also explore this case and propose new methods as well as sixth-order methods with complex coefficients. In particular, highly optimized sixth-order schemes for near integrable systems using positive real part complex coefficients with and without modified potentials are presented. A time-stepping variable order algorithm is proposed and numerical results show the enhanced efficiency of the new methods.
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Subjects:
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Symplectic integrators
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Ecuations
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Schemes
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Systems
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Steps
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Journal of Chemical Physics. (issn:
0021-9606
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DOI:
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10.1063/1.4821126
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Publisher:
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American Institute of Physics (AIP)
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Publisher version:
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http://dx.doi.org/10.1063/1.4821126
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Project ID:
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Ministerio de Ciencia e Innovacion (Spain) MTM2010-18246-C03
Qatar National Research Fund (NPRP) NPRP 5-674-1-114
FPU fellowship AP2009-1892
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Thanks:
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We wish to acknowledge Ander Murua and Joseba Makazaga for providing the methods T86<INF>9</INF> and V86<INF>9</INF>. This work has been partially supported by Ministerio de Ciencia e Innovacion (Spain) under Project ...[+]
We wish to acknowledge Ander Murua and Joseba Makazaga for providing the methods T86<INF>9</INF> and V86<INF>9</INF>. This work has been partially supported by Ministerio de Ciencia e Innovacion (Spain) under Project MTM2010-18246-C03 and by a grant from the Qatar National Research Fund (NPRP) #NPRP 5-674-1-114. P.B. also acknowledges the support through the FPU fellowship AP2009-1892.
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Type:
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Artículo
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