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

Nonuniversal Effects in Bose-Einstein CondensationIn 1924 Albert Einstein predicted the conception of a special type 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-density Bosonic float. This young experimental breakthrough has led to renewed theoretical interest in BEC. The focus of my research is to more consummately de conditionine basic properties of undiversified Bose gases. In particular nonuniversal effects of the energy density and condensate member will be explored. The validity of the theoretical predictions obtained is verified by similarity to numerical data from the paper beginitGround State of a Homogeneous Bose Gas A Diffusion Monte Carlo Calculation peculiarityit by Giorgini, Boronat, and Casulleras. endabstract%dedicateTo my parents for their supporting me through college,%to immortal for all the mysteries of physics, and to Jammie for her%unconditional lo ve.%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 amongst the atoms can be characterized by a single occur $a$ called the S-wave scattering length. This property is known as beginituniversalityendit. Increasingly accurate measurements will show deviations from universality. These effects are due to sensitivity to aspects of the interatomic interactions another(prenominal) than the scattering length. These effects are known as beginitnonuniversalendit effects. intensifier theoretical investigations into the homogeneous Bose gas revealed that properties could be calculated using a low-density expansion 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 Bogoliubov course creditBog. 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 reach 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 scene relevant to this problem is presented. Section III is a brief compend of the numerical data from Giorgini, Boronat, and Casulleras.