Software

Splitting methods

• Splitting methods for near-integrable systems
• Symplectic splitting methods for the time-dependent (autonomous) Schrödinger equation
• Symplectic splitting methods for the time-dependent (non-autonomous) Schrödinger equation
• An efficient algorithm based on symplectic splitting for computing the action of the exponential of a skew-Hermitian matrix on a vector
• Splitting methods with complex coefficients for evolution equations
• Splitting methods in the imaginary time propagation technique

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Exponential perturbation expansions

• Computation of the Magnus series
• A unitary perturbative expansion based on Lie-Deprit
• Exponential perturbative expansions and coordinate transformations: a Mathematica code for the Boch-Siegert Hamiltonian
• A Mathematica code generating explicit expressions and recurrences for the Wilcox expansion

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Computation of the exponential of a matrix

• A general purpose algorithm to compute the exponential of a matrix (intended to replace expm)
• A specific algorithm to compute the exponential of a skew-Hermitian matrix

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The BCH formula

• The BCH formula and the symmetric BCH formula up to terms of grade 20 in two different basis of the free Lie algebr. Optimized expressions up to grade 10 in terms of right-nested commutators

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Hybrid Monte Carlo

• Code for the paper Split HMC Revisited.

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