Nonuniversal Effects in Bose-Einstein Condensation :: Albert Einstein Gases Science Essays

Nonuniversal Effects in Bose-Einstein CondensationIn 1924 Albert Einstein predicted the existence of a special image of matter now known as Bose-Einstein condensation. However, it was not until 1995 that simple BEC (Bose-Einstein condensation) was observed in a low- niggardliness Bosonic bobble. This recent experimental breakthrough has led to regenerate theoretical interest in BEC. The focus of my research is to more accurately de terminationine basic properties of homogeneous Bose gases. In particular nonuniversal effects of the energy density and condensate fraction will be explored. The validity of the theoretical predictions obtained is verified by comparison to numerical data from the paper beginitGround rural area of a Homogeneous Bose Gas A Diffusion monte Carlo Calculation endit by Giorgini, Boronat, and Casulleras. endabstract%dedicateTo my parents for their supporting me through college,%to perfection for all the mysteries of physics, and to Jammie for her%unconditio nal love.%newpage%tableofcontentsnewpagesectionIntroductionThe Bose-Einstein condensation of trapped atoms allows the experimental study of Bose gases with high precision. It is well known that the dominant effects of interactions between the atoms mass be characterized by a single number $a$ called the S-wave scattering length. This property is known as beginituniversalityendit. Increasingly accurate measurements will destine deviations from universality. These effects are due to sensitivity to aspects of the interatomic interactions other than the scattering length. These effects are known as beginitnonuniversalendit effects. Intensive theoretical investigations into the homogeneous Bose gas revealed that properties could be calculated using a low-density working out in powers of $sqrtna3$, where $n$ is the number density. For example the energy density has the expansionbeginequationfracEN = frac2 pi na hbar2m Bigg( 1 + frac12815sqrtpisqrtna3 + frac8(4pi-3sqrt3)3na3 (ln(na3)+c) + ... Bigg)labelenendequationThe first term in this expansion is the mean-field approximation and was calculated by grind to a haltoliubov citeBog. The corrections to the mean-field approximation can be calculated using perturbation theory. The coefficient of the $(na3)3/2$ term was calculated by Lee, Huang, and Yang citeLHY and the last term was first calculated by Wu citewu. Hugenholtz and Pines citehp buzz off shown that the constant $c_1$ and the higher-order terms in the expansion are all nonuniversal. Giorgini, Boronat, and Casulleras citeGBC have studied the ground state of a homogeneous Bose gas by exactly solving the N-bodied Schrodinger (to within statistical error) using a diffusion Monte Carlo method. In section II of this paper, theoretical background relevant to this problem is presented. Section III is a brief summary of the numerical data from Giorgini, Boronat, and Casulleras.