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Sergio Blanes

Publications and source records attributed to Sergio Blanes.

3 recordsLinked to original sources
PubMed2006

Symplectic splitting operator methods for the time-dependent Schrodinger equation.

We present a family of symplectic splitting methods especially tailored to solve numerically the time-dependent Schrodinger equation. When discretized in time, this equation can be recast in the form of a classical Hamiltonian system with a Hamiltonian function corresponding to a generalized high-dimensional separable harmonic oscillator. The structure of the system allows us to build highly efficient symplectic integrators at any order. The new methods are accurate, easy to implement, and very stable in comparison with other standard symplectic integrators.

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PubMed2002

Symplectic maps for approximating polynomial Hamiltonian systems.

We study how to approximate polynomial Hamiltonian systems by composition of symplectic maps. Recently, a number of methods preserving the symplectic character have appeared. However, they are not completely satisfactory because, in general, they are computationally expensive, very difficult to obtain or their accuracy is relatively low. The efficiency of a numerical method depends on both its computational cost and its accuracy. Polynomial Hamiltonians are separable in exactly solvable parts, and this can be done in many different ways. Here we study how to find a separation for the Hamiltonian in a small number of cheaply computed terms. Since the proposed methods depend on some free parameters, we also indicate how to choose these parameters in order to improve the accuracy without increasing the computational cost.

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