The Complete Characterization of Fourth-Order Symplectic Integrators with Extended-Linear Coefficients

Abstract

The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of these {\it extended-linear} symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and non-forward fourth-order algorithms with arbitrary number of operators. Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.

12 pages, 2 figures, submitted to Phys. Rev. E, corrected typos

References in corpus (6)

• Gradient Symplectic Algorithms for Solving the Schroedinger Equation with Time-Dependent Potentials
• On the construction of high-order force gradient algorithms for integration of motion in classical and quantum systems
• Fourth-Order Algorithms for Solving the Imaginary Time Gross-Pitaevskii Equation in a Rotating Anisotropic Trap
• Quantum Statistical Calculations and Symplectic Corrector Algorithms
• Forward Symplectic Integrators and the Long Time Phase Error in Periodic Motions
• Short time evolved wave functions for solving quantum many-body problems

Cited by in corpus (5)

• High-order Path Integral Monte Carlo methods for solving quantum dot problems
• Brownian Dynamics of charged particles in a constant magnetic field
• The physics of symplectic integrators: perihelion advances and symplectic corrector algorithms
• A Fundamental Theorem on the Structure of Symplectic Integrators
• A quantum Monte Carlo based density functional for Dysprosium dipolar system