Application of Deconvolution in Path Integral Simulations

In path integral molecular dynamics (PIMD) simulations, atoms are represented by several replicas connected with harmonic springs, so additional vibrations appear beyond the physical vibrations because of the normal mode frequencies coming from the springs of the ring polymer. In harmonic approximation, the frequencies of these internal modes can be determined exactly from the physical frequencies. We show that this formal effect of the path integral simulations on the vibrations can be considered as a convolution if we use the square of the frequency as an independent variable. This convolution can be represented as a matrix multiplication. The potential of the formalism is demonstrated in two applications. We present an alternative method to determine the power spectrum of thermostats used in PIMD simulations. We also show that in simple anharmonic model systems, the physical frequencies can be obtained from ring polymer molecular dynamics simulations by deconvolution, even in cases where spurious resonances appear.