New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

Speciation of Pu(III) in the environmental system humic substances-groundwater-kaolinite

For the safety assessments of nuclear waste repositories, the possible migration of the radiotoxic waste into environment must be considered. Since plutonium is the major contribution at the radiotoxicity of spent nuclear waste, it requires special care with respect to its mobilization into the groundwater. Plutonium has one of the most complicated chemistry of all elements. It can coexist in 4 oxidation states parallel in one solution. In this work is shown that in the presence of humic substances it is reduced to the Pu(III) and Pu(IV). This work has the focus on the interaction of Pu(III) with natural occurring compounds (humic substances and clay minerals bzw. Kaolinite), while Pu(IV) was studied in a parallel doctoral work by Banik (in preparation). As plutonium is expected under extreme low concentrations in the environment, very sensitive methods are needed to monitor its presence and for its speciation. Resonance ionization mass spectrometry (RIMS), was used for determining the concentration of Pu in environmental samples, with a detection limit of 106- 107 atoms. For the speciation of plutonium CE-ICP-MS was routinely used to monitor the behaviour of Pu in the presence of humic substances. In order to reduce the detection limits of the speciation methods, the coupling of CE to RIMS was proposed. The first steps have shown that this can be a powerful tool for studies of pu under environmental conditions. Further, the first steps in the coupling of two parallel working detectors (DAD and ICP_MS ) to CE was performed, for the enabling a precise study of the complexation constants of plutonium with humic substances. The redox stabilization of Pu(III) was studied and it was determined that NH2OHHCl can maintain Pu(III) in the reduced form up to pH 5.5 – 6. The complexation constants of Pu(III) with Aldrich humic acid (AHA) were determined at pH 3 and 4. the logß = 6.2 – 6.8 found for these experiments was comparable with the literature. The sorption of Pu(III) onto kaolinite was studied in batch experiments and it was determine dthat the pH edge was at pH ~ 5.5. The speciation of plutonium on the surface of kaolinite was studied by EXAFS/XANES. It was determined that the sorbed species was Pu(IV). The influence of AHA on the sorption of Pu(III) onto kaolinite was also investigated. It was determined that at pH < 5 the adsorption is enhanced by the presence of AHA (25 mg/L), while at pH > 6 the adsorption is strongly impaired (depending also on the adding sequence of the components), leading to a mobilization of plutonium in solution.