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

Nonuniversal Effects in Bose- superstar CondensationIn 1924 Albert Einstein predicted the existence of a special type of matter now cognise as Bose-Einstein condensation. However, it was not until 1995 that simple BEC (Bose-Einstein condensation) was observed in a low density Bosonic gas. This recent experimental breakthrough and through has led to renewed suppositious take in BEC. The focus of my research is to more accurately de full termine fundamental properties of like Bose gases. In particular nonuniversal effects of the energy density and condensing fraction will be explored. The validity of the theoretical predictions obtained is verified by comparison to numerical data from the paper dejectitGround put up of a Homogeneous Bose Gas A Diffusion Monte Carlo counting endit by Giorgini, Boronat, and Casulleras. endabstract%dedicateTo my parents for their supporting me through college,%to God for all the mysteries of physics, and to Jammie for her%unconditional love.% newpage%tableofcontentsnewpagesectionIntroductionThe Bose-Einstein condensation of detain atoms allows the experimental study of Bose gases with high precision. It is well known that the dominant effects of interactions between the atoms can be characterized by a single derive $a$ called the S-wave scattering length. This property is known as beginituniversalityendit. progressively accurate measurements will show deviations from universality. These effects are due to aesthesia 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 apply a low-density expansion in powers of $sqrtna3$, where $n$ is the number density. For example the energy density has the expansionbegin parfracEN = frac2 pi na hbar2m Bigg( 1 + frac12815sqrtpisqrtna3 + frac8(4pi-3sqrt3)3na3 (ln(na3)+c) + ... Bigg)labelene ndequationThe first term in this expansion is the mean-field approximation and was calculated by bogoliubov citeBog. The corrections to the mean-field approximation can be calculated employ swage theory. The coefficient of the $(na3)3/2$ term was calculated by Lee, Huang, and Yang citeLHY and the pop off term was first calculated by Wu citewu. Hugenholtz and Pines citehp have 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 skeleton summary of the numerical data from Giorgini, Boronat, and Casulleras.