The Symplectic Splitting Method

More documents

Recommendations

Info

The Schrödinger equation We consider different families of Geometric Integrators for solving the SE The solution of the discretised autonomous equation is given by where c = (c 1,…, c N) T C N and H = T + V R N×N Hermitian matrix. Fourier methods are frequently used is the fast Fourier transform (FFT)
The Methods Considered I - If the solution is not smooth: methods which involve products H c Polynomial approximations to the action of the exponential on a vector 1 – Taylor 2 – Chebyshev II - If the solution is smooth: to split H=T+V 3 – Splitting (real + imaginary parts) High-order Splitting-decomposition methods (with possible complex coefficients)
Page 1: Splitting and composition methods f
Page 5 and 6: The Methods Considered I - If the s
Page 7 and 8: The Taylor Method An m-stage Taylor
Page 9 and 10: The Chebyshev Method The Chebyshev
Page 11 and 12: Taylor order tol=inf tol=10 -8 tol=
Page 13 and 14: The linear time dependent SE with H
Page 15 and 16: The Symplectic Splitting Method The
Page 17 and 18: Error bounds: Splitting Methods: va
Page 19 and 20: LOG(ERROR) 0 -2 -4 -6 -8 -10 -12 Po
Page 21 and 22: LOG(ERROR) 0 -2 -4 -6 -8 -10 -12 Po
Page 23 and 24: References SB, F. Casas, and A. Mur
Page 25 and 26: Splitting methods with complex coef
Page 27 and 28: Splitting methods with complex coef
Page 29 and 30: Splitting for perturbed systems Add
Page 31 and 32: Splitting for perturbed systems Add

The Symplectic Splitting Method

Create successful ePaper yourself

Delete template?

Save as template?