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Heat semigroup representation of Laplacian
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DOI：10.1016/j.jcp.2026.114878.png)
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Abstract
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This work introduces a heat semigroup representation of the Laplace operator aimed at enabling stable time evolution methods within multiresolution analysis. While convolution-based Laplacian approximations are not universally advantageous, they become attractive in multiwavelet frameworks where heat equation solvers are highly optimized. The primary motivation is to support iterative application in dynamical quantum simulations, where propagators constructed from repeated multiwavelet differentiation suffer from noise amplification. The proposed representation is validated through self-consistent field calculations, demonstrating compatibility with electronic structure theory, and through time propagation of a harmonic oscillator, illustrating stable iterative behavior. These results indicate the feasibility of heat-based Laplacian representations as a foundation for future multiwavelet approaches to attosecond dynamics.
Keywords:
Schr & ouml
dinger equation
Heat semigroup
Laplace operator
Multiwavelets
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