Dynamics of doped [4]He and [3]He clusters from reptation quantum Monte Carlo

In this thesis we will address these open issues in the spectroscopy of doped 4He clusters. Some of the techniques developed to this purpose will turn out to be instrumental in tackling one of the hardest problems in quantum simulation today, namely the simulation of interacting fermions. In particular, we will address the splitting of roto-vibrational lines observed in the spectra of small CO@4HeN clusters for some cluster sizes N [25], that led in turn to ambiguous assignments of experimental lines around this size range [26]. Then, we will investigate the nature of the weak satellite band, experimentally seen to accompany the roto-vibrational line in the infrared spectrum of CO2 solvated in 4He nanodroplets [27]. Further, the controversial convergence of CO effective rotational constant towards the nanodroplet limit will be discussed. Finally, we will study the effect that particle exchanges in a quantum solvent exhibit on the spectra of embedded molecules. This physical issue is particularly interesting because the NCRI manifests itself in quantum clusters already for extremely small system sizes. Experimentally, this effect was studied by Grebenev et al. [28, 29] by comparing the rotational spectra of OCS molecule solvated with para-hydrogen molecules, that are indistinguishable bosons, and ortho-deuterium molecules, an essentially distinguishable bosonic mixture. On the theoretical side, this issue was tackled by finite temperature simulations of N2O solvated with distinguishable particles [11]. In this thesis we will address it by zero-temperature simulations of doped 3He clusters. The thesis is organized as follows. Quantum Monte Carlo methods are introduced in Chapter 1, with emphasis on RQMC. In Chapter 2 we present the implementation of RQMC for doped He clusters, together with several technical details of the simulation. Chapter 3 addresses the approach of CO effective rotational constant to its nanodroplet value. In Chapter 4 we cope with fine spectral features such as line splittings in small CO@4HeN clusters and the satellite band in the infrared spectra of CO2 solvated in 4He nanodroplets. To this purpose, we introduce symmetry-adapted, imaginary-time correlation functions (SAITCFs), that are specifically devised for an explicit theoretical characterization of individual excitations, as well as for an enhanced computational efficiency in the calculation of weak spectral features. Also, we show how RQMC data help to discriminate between different assignments of experimental lines proposed for CO@4HeN clusters around the cluster size where one of the splittings is observed. In Chapter 5 we address the effect of particle statistics on the rotational spectra of 3He-solvated molecules. We introduce a new method, based on a generalization of SAITCF approach that allows us to access rotational states of systems obeying Fermi statistics, still performing RQMC simulations for bosons. We apply this method to CO2 solvated with 3He atoms. Our preliminary results indicate that a certain amount of NCRI is found also in these fermionic clusters.