LOW TEMPERATURES

Author: CAZORLA SILVA CLAUDIO.
Year: 2005.
University: POLITÉCNICA DE CATALUÑA.
Place of defense: AULA DE TELEENSENYAMENT EDIFICI B.3.
Place of preparation: EDIFICI B5 DESPATX B5-011 NORD.

Summary: Quantum solids conform an intriguing class of crystals where quantum effects have a leading relevance. Contrarily to their classical counterparts, quantum solids present an unusually large kinetic energy and atomic mean squared displacement of the particles around the equilibrium positions of the crystalline lattice. By large it is understood, a kinetic energy similar in magnitude to short-range interactions and a mean squared displacementcomparable to the distance between nearest positions in the perfect lattice (large Lindemann's ratio). In fact, the constituents of these solids are characterized by small atomic masses, and the interactions acting among them are weakly attractive. From a thermodynamic point of view, quantum solids are described by large compressibilities, low Debye temperatures and speeds of sound, non-ordinary melting properties, anharmonicity, etc. Point and line defects (vacancies, dislocations, etc.) are easily formed on their interior due to the wide excursions of the atoms around the lattice sites. These structural defects are expected to exist in quantum solids even at absolute zero temperature. Some illustrative examples of quantum solids are 4He, 3He, H2, D2, LiH and LiD. In the outstanding case of solid helium, the possibility of superfluid-like behaviour has resulted in a long-standing topic of intense speculation. Recent experiments carried out by E. Kim and M. H. Chan in solid 4He, seem to allow the existence of a practically suppressed superfluid fraction below 0.2K (~1-2%). Early in the 60's, Quantum Monte Carlo (QMC) methods emerged in close relation to quantum many-body problems posed in the field of condensed matter. The QMC approach is a fully quantum one (it does not rely on any basic assumption or approximation), which it is best suited to deal with systems where quantum effects are dominant. The basic strategy underlying QMC methods is stochastic, that is, random number generation and probability theory are inherent to all of them. In this thesis, two different QMC techniques have been used to investigate the ground-state properties of quantum solids, namely, variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). The VMC approach relies on the variational principle and it provides accurate estimations of the total energy based on reliable models for the ground-state wave function. On the other hand, the DMC method allows us to solve exactly the imaginary time-dependent Schrödinger equation of interest, providing asymptotically its ground-state solution. Accurate estimations of the total energy and expected values of operators which commute with the Hamiltonian are yielded in this scenario with affordable computational effort. Comprehensive studies of the energy and structural properties of the solids cited above (made the exception of 3He) and Ne, which is a crystal in the middle-way between quantum and classical behaviour, have been carried out with the two mentioned QMC approaches. In the case of solid 4He, we have also tried to shed more light on the issue of superfluidity. Actually, the species investigated in the present work turn out to be representative elements of the quantum solid class.