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MANY STUDIES ON BODY ATOMIC QUANTUM SYSTEMSAuthor: MUR PETIT JORDI. Year: 2005. University: BARCELONA [ www.ub.es]. Place of defense: FACULTAT DE FÍSICA. Place of preparation: FACULTAT DE FÍSICA. Summary: This thesis presents a series of studies of atomic systems where quantum effects are especially prominent. These studies have been carried out by applying various techniques of theoretical physics of many bodies. First, it has studied the possibility of the existence of a transition superfluida in a gas ultrafrío atoms fermiónicos through a generalization of the theory of Bardeen-Cooper-Schrieffer (BCS). Once you have determined that this possibility depends heavily on the asymmetry in density between the two species has been analyzed how to solve this limitation assuming that the ground state of the system breaking one or more spatial symmetries spontaneously. It has proposed a pilot scheme for determining the presence of one of these phases. Finally, it has studied the possibility that the transition to superfluidez takes place in a system consisting of a single species fermiónica 3en contact with a kind bosónica. In particular, it has analyzed the case of a mixture of two-dimensional and it has been considered the possibility of experimental realization of such a system. In a second part, has been studying the dynamics of a Bose-Einstein condensate with the degree of freedom of spin-free evolve into a trap optic cuasi-unidimensional. By formulating a field environment, it has been determined that the interaction intratómica can lead to changes in populations of the various states hiperfinos of trapped atoms, and the formation of spin domains. It has made an approach to the inclusion of temperature effects on the dynamics. Finally, it has undertaken the study of a quantum system strongly correlated. Specifically, it has studied the ground state of two-dimensional systems of helium-4 in two dimensions. This study was divided into two parts. First, using Monte Carlo techniques, it has been determined the status of key drops of finite size, and it has been estimated linear tension. This information has subsequently been used for the construction of a functional density that has enabled the study of larger drops, as well as ways homegéneo and semiinfinito.
STUDY OF HELIUM DROPLETS USING QUANTUM TECHNIQUES MOUNT CARLOSummary: Helium systems at zero temperature are strongly correlated neutral systems which can only be described by means of quantum mechanics. The existence of the two isotopes 4He and 3He allows the comparison between the quantum effects due to different statistics, bosonic and fermionic. In this Thesis, an analysis of Helium droplets has been done. Throughout this work, both energetic and structural properties of systems with different number of particles N are obtained by means of the Quantum Monte Carlo techniques (Variational and Diffusion Monte Carlo â VMC and DMC-). Several studies on Helium droplets have been published in the last years, most of them using the mean field theory (as the Density Functional) and variational approaches (as VMC). In the case of 4He, also exact DMC results have already been reported, actually, a great number of works have described with high accuracy the ground state of this bosonic system. The appearance of magic numbers from experimental point of view has motivated the study of 4He droplets, and one chapter of this Thesis is focused on this bosonic system. We have carried out a one-by-one energetic study in the range from 20 to 30 particles using the DMC technique to discuss the existence of magic numbers. On the other hand, a brief study about vortices is also done; using out code, one can calculate the energy of a droplet with one vortex inside (EV) and, therefore, the energy of a vortex (EV -E0). About 3He droplets, the sign problem makes their study quite more difficult, for this reason, the number of works is considerably smaller than in the bosonic case. One aim of this thesis was to write a DMC code using both Fixed and Released Node approximations (FN and RN) able to perform high accurate calculations of energetic and structural properties of these finite fermionic systems. A complete optimization of the trial wave function used to describe the system is presented and different types of functions are compared in order to choose the most appropriate; in this way, a Jastrow-Slater (JS) wave function provides the best results and other approximations such as BCS can not improve the JS description. An exhaustive analysis of the correlation effects has been done, where one can see that backflow correlations are essential to describe 3He droplets. This conclusion is reinforced when using the RN technique which has been applied to the N=40 case; despite the bosonic component overwhelms the fermionic signal, the RN curve shows a reduction of the initial slope by a factor of two when backflow correlations are present. Finally, an exhaustive one-by-one study of the droplets in the range from 29 to 70 atoms is presented; their energy and the density profiles are reported. Concerning the energy, two main conclusions can be derived from these results, on the one hand, the minimum number of atoms necessary to form a bound system is 30 and, on the other hand, changes in the slope of the energy curve at N=30 and 40 indicates the existence of magic numbers. The statistics effects are clear when comparing both 4He and 3He profiles, the fermionic droplet being much less dense due to the Pauli principle. This thesis presents highly accurate values for Helium droplets properties at zero temperature by means of QMC techniques. In the 3He case, an exhaustive analysis of the system has been done in order to understand and describe this fermionic strongly correlated system.
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