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Abstract
A wavelet formulation of path integral Monte Carlo (PIMC) is constructed. Comparison with Fourier path integral Monte Carlo is presented using simple one-dimensional examples. Wavelet path integral Monte Carlo exhibits a few advantages over previous methods for PIMC. The efficiency of the current method is at least comparable to other techniques.
Highlights
Path integral Monte CarloPIMC1 combines the conceptual clarity in linking quantum mechanics to classical Lagrangian dynamicspath integral[2] with computational power of Monte Carlo sampling method.[3]
After presenting a brief description of different path integral Monte Carlo methods and relevant portion of wavelet theory, we have established a wavelet formulation of path integral Monte Carlo method
In actual implementation of these wavelets, readily available fast wavelet transform routines, which are based on the idea of filters, were adopted
Summary
Path integral Monte CarloPIMC1 combines the conceptual clarity in linking quantum mechanics to classical Lagrangian dynamicspath integral[2] with computational power of Monte Carlo sampling method.[3]. Unlike plane waves, which are a basis for Fourier analysis, wavelets are localized in both time and position For this reason, wavelets are better suited for describing abrupt changes in signals. Mexican hat wavelet is well suited for the represention of the electronic wave functions due to their smoothness, the lack of an FWT for these nonorthogonal bases reduces their overall utility. Following this application of wavelet theory to electronic structure calculation, several other researchers used orthonormal wavelet bases in self-consistent calculation and molecular dynamics calculation.[9,10]. We conclude with the findings of this endeavor and future direction of research
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