Simulações Monte Carlo de integrais de trajetória : propriedades elásticas do 4He sólido / Path integrals Monte Carlo simulations : elastic properties of 4He

AUTOR(ES)
FONTE

IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia

DATA DE PUBLICAÇÃO

30/11/2010

RESUMO

The path-integral Monte Carlo (PIMC) method is a sophisticated approach for the simulation of many-body quantum systems. In particular, it has been extensively used for the study of manybody bosonic systems such as 4He. The main objective of the present dissertation is to apply the PIMC method to determine the elastic constants of solid 4He in its hcp phase. These properties are very important in view of their apparent involvement in the phenomenon of supersolidity in solid 4He. To realize this objective we utilize the software package PIMC++, which is an implementation of the PIMC method written in C++, developed in the group of Prof. David Ceperley. First, we carry out a number of basic tests, computing the total energy and heat capacity of an ideal gas of bosons, a system for which analytical results are available. Subsequently, we consider the liquid phase of 4He described by the Aziz pair potential, determining the energy per particle, the condensate fraction and superfluid density below 4 K under conditions of saturated vapor pressure. In addition, we compute the pair correlation function and the structure factor. All properties show good agreement with experimental data. After these preliminary tests, we determine the elastic constants of solid 4He in its hcp phase. To this end we implement the scheme due to Parrinello and Rahman, which allows the use of non-orthorhombic computational cells in PIMC++. In addition, we develop and implement an expression for the stress tensor observable within the path-integral formalism. After these technical developments, we determine the elastic constants by means of a series of tension/compression and shear deformations, measuring the corresponding internal stress states. Next, using the definition in terms of the linear relationship between stress and strain, we compute the elastic constants. The results obtained for 3 different densities at a temperature of 1K demonstrate that the Aziz model captures the fundamental characteristics of the elastic properties of 4He in the hcp phase

ASSUNTO(S)

elasticidade do hélio sólido constantes elásticas simulação de monte carlo elasticity of solid helium elastic constants monte carlo simulations

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