# Symplectic integrators for the multichannel SchrÃ¶dinger equation

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- Application of symplectic integrator to stationary reactive-scattering problems: Inhomogeneous... Takahashi, Kin'ya; Ikeda, Kensuke S. // Journal of Chemical Physics;3/15/1997, Vol. 106 Issue 11, p4463
Discusses the application of symplectic integrator to stationary reactive-scattering problems using the inhomogeneous Schrodinger equation approach. Computation of the scattering eigenstates by integrating the Schrodinger equation with the FFT-symplectic integrator scheme; Efficient wave source...

- Adiabatic and post-adiabatic representations for multichannel SchrÃ¶dinger equations. Aquilanti, Vincenzo; Cavalli, Simonetta; Sevryuk, Mikhail B. // Journal of Mathematical Physics;Feb94, Vol. 35 Issue 2, p536
The properties of the adiabatic representation of a multichannel SchrÃ¶dinger equation are analyzed by exploiting the Hamiltonian and symplectic nature of the coefficient and transformation matrices, respectively. Use of this algebraic structure of the problem is shown to be in line with an...

- Phase fitted symplectic partitioned Runge-Kutta methods for the numerical integration of the SchrÃ¶dinger equation. Monovasilis, Th. // Journal of Mathematical Chemistry;Aug2012, Vol. 50 Issue 7, p1736
In this work we consider explicit symplectic partitioned Runge-Kutta methods with five stages for problems with separable Hamiltonian. We construct three new methods, one with constant coefficients of eight phase-lag order and two phase-fitted methods.

- From Efficient Symplectic Exponentiation of Matrices to Symplectic Integration of High-dimensional Hamiltonian Systems with Slowly Varying Quadratic Stiff Potentials. Tao, Molei; Owhadi, Houman; Marsden, Jerrold E. // Applied Mathematics Research eXpress;Jun2011, Vol. 2011 Issue 2, p242
We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for constant quadratic stiff potentials). This method is based on the highly nontrivial introduction of two efficient...

- Time behaviour near to spectral singularities. Heiss, W. D. // European Physical Journal D -- Atoms, Molecules, Clusters & Opti;Nov2010, Vol. 60 Issue 2, p257
Spectral singularities such as exceptional points invoke specific physical effects. The present paper focuses upon the time dependent solutions of the SchrÃ¶dinger equation. In a simple model it is demonstrated that - depending on initial conditions - within close proximity of exceptional...

- A NOTE ON CONSTRUCTION OF HIGHER-ORDER SYMPLECTIC SCHEMES FROM LOWER-ORDER ONE VIA FORMAL ENERGIES. Yi-fa Tang // Journal of Computational Mathematics;Nov99, Vol. 17 Issue 6, p561
Presents a study which proved by the help of formal energies only that one can improve the order of any symplectic scheme by modifying the Hamiltonian symbol H. Formal energies of symplectic schemes; Fundamental theorem; Examples of H modification.

- Action principle and the Hamiltonian formulation for the Maxwell--Vlasov equations on a... Fla, Tor // Physics of Plasmas;Aug94, Vol. 1 Issue 8, p2409
Explains the formulation of an action principle for the Maxwell-Vlasov (MV) equation in terms of the Maxwell fields and the generating function for deviations from a reference distribution function which labels a symplectic leaf. Formal fields suitable for variations; Hamiltonian formulation of...

- Total variation in Hamiltonian formalism and symplectic-energy integrators. Chen, Jing-Bo; Guo, Han-Ying; Wu, Ke // Journal of Mathematical Physics;Apr2003, Vol. 44 Issue 4, p1688
We present a discrete total variation calculus in Hamiltonian formalism in this paper. Using this discrete variation calculus and generating functions for the flows of Hamiltonian systems, we derive symplectic-energy integrators of any finite order for Hamiltonian systems from a variational...

- Properties of the symplectic structure of general relativity for spatially bounded spaceâ€“time regions. Anco, Stephen C.; Tung, Roh S. // Journal of Mathematical Physics;Aug2002, Vol. 43 Issue 8, p3984
We continue a previous analysis of the covariant Hamiltonian symplectic structure of general relativity for spatially bounded regions of space-time. To allow for wide generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike two-surface....