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|Title:||SEMICLASSICAL PARTICLE DENSITIES FOR MANY-FERMION SYSTEMS||Authors:||CHAU THANH TRI||Keywords:||quantum gases, density functional theory, semiclassical fermion densities, ultra-cold atoms, semiclassical physics, Thomas-Fermi||Issue Date:||18-Aug-2016||Citation:||CHAU THANH TRI (2016-08-18). SEMICLASSICAL PARTICLE DENSITIES FOR MANY-FERMION SYSTEMS. ScholarBank@NUS Repository.||Abstract:||The present thesis fits within a self-consistent density-functional scheme for finding the particle density for interacting many-fermion systems by developing a consistent method for finding the semiclassical density in any dimension from the effective potential beyond the Thomas-Fermi density. This is motivated by the dazzling performance of the semiclassical density for 1D potentials with two turning points derived by [Ribeiro et al., PRL 114, 050401 (2015)], which unfortunately cannot be generalized to higher dimensions as it requires the wave function to be patched. We propose a method for finding the density from the quantum propagator, approximated in two ways: via the Suzuki-Trotter decomposition of the time-evolution operator or the van Vleck-Gutzwiller propagator. We recover from the latter among other things the leading term of Ribeiro et al.’s density. The densities obtained from the former approximation require no patching and hence apply to anisotropic potentials in higher dimensions.||URI:||http://scholarbank.nus.edu.sg/handle/10635/134439|
|Appears in Collections:||Master's Theses (Open)|
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