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In this thesis we have combined the idea of cluster expansion and path integration to develop the quantum version of cluster and virial expansion. We derive a diagrammatic series expansion for different thermodynamic quantities like free energy, chemical potential and pair distribution function and show that the diagrammatic expansion is linked. This expansion in n-body clusters can also be thought of as a power series expansion in the particle density. We first present the results for the pair distribution function by evaluating it up to a first few orders in particle density and show that there is systematic order-by-order improvement. Second, we use a Pade` resummation scheme in momentum space to extrapolate to infinite order. This scheme is constructed in such a way so that it yields the calculated order by order expansion terms and the classical limit correctly. We have also used our proposed quantum version of Hypernetted-chain (HNC) equations to calculate the observables by solving self-consistently a set of integral equations which sum a certain class of contributing diagrams which resemble a “hypernetted” network. We have tested our summation schemes on a Lennard-Jones and a hard-sphere system containing distinguishable particles and our results agree very well with those obtained from the path-integral Monte Carlo simulation. We have also demonstrated the applicability to a system of identical particles by applying it to the bosonic system of 4He particles. Our method is easily applicable to the case of a short-range singular potential where the established analytical and semi-analytical tools of many-body perturbation theory and quantum statistical mechanics cannot be applied in a straightforward manner.
A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Efstratios Manousakis, Professor Directing Dissertation; Naresh Dalal, University Representative; Vladimir Dobrosavljevic, Committee Member; Bernd A. Berg, Committee Member; David Van Winkle, Committee Member.
Florida State University
Bhardwaj, A. (no date). Linked Cluster Expansion of the Many-Body Path-Integral. Retrieved from https://purl.lib.fsu.edu/diginole/2020_Spring_Bhardwaj_fsu_0071E_15848