Quantum Correction to the Gross-Pitaevskii Equation in a Bose-Eisntein Condensate(The 8th Symposium on Non-Equilibrium Statisitical Physics)

Abstract

調和振動子型ポテンシャル中のアルカリ原子のBose-Einstein凝縮(BEC)の実験に対する多くの理論的考察はGross-Pitaevskii(GP)方程式に基づいている.この報告書では, GP方程式を超える試みとして,場の理論による定式化を行った.まず,零度で定式化し,それをThermo Field Dynamicsにより有限温度に拡張する.非摂動的な定式化のために必要な数値計算も行い,例として, GP方程式に対する1-ループレベルの補正を計算した.また,凝縮相に対する量子・温度補正の影響も評価した.

So far many theoretical considerations for experiments of Bose-Einstein condensation (BEC) of alkali atoms in harmonic traps are based on the Gross-Pitaevskii (GP) equation. In this report, we attempt to formulate the BEC in the language of quantum field theory in order to go beyond the approximation of GP equation. First the formulation at zero-temperature is presented, and then it is extended to finite-temperature case by means of Thermo Field Dynamics. Numerical calculations, which are inevitable even in the unperturbative formulation of our approach, are performed. For illustration, the corrections at one-loop level to the original GP equation are given. We also calculate the effects of quantum and thermal fluctuations to the distribution of condensed atoms numerically.