Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation

[EN] We present a new family of fourth-order splitting methods with positive co-efficients especially tailored for the time integration of linear parabolic problems and, in particular, for the time dependent Schrodinger equation, both in real and imaginary time. They are based on the use of a double...

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Detalles Bibliográficos
Autores: Blanes Zamora, Sergio|||0000-0001-5819-8898, Casas, Fernando, González, Cesáreo, Thalhammer, Mechthild
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/212320
Acceso en línea:https://riunet.upv.es/handle/10251/212320
Access Level:acceso abierto
Palabra clave:Schrodinger equation
Imaginary time propagation
Parabolic equations
Operator splitting methods
Modified potentials
MATEMATICA APLICADA
Descripción
Sumario:[EN] We present a new family of fourth-order splitting methods with positive co-efficients especially tailored for the time integration of linear parabolic problems and, in particular, for the time dependent Schrodinger equation, both in real and imaginary time. They are based on the use of a double commutator and a modified processor, and are more efficient than other widely used schemes found in the literature. Moreover, for certain potentials, they achieve order six. Several examples in one, two and three dimensions clearly illustrate the computational advantages of the new schemes.