Particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
Particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
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粒子数守恒 Bogoliubov 方法证明了高度凝聚玻色气体的时间相关 Gross-Pitaevskii 方程的有效性
DOI：
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发表时间：
1997
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影响因子：
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通讯作者：
C. Gardiner
中科院分区：
文献类型：
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作者：
C. Gardiner
推广了玻色凝聚气体激发谱的Bogoliubov方法，使之适用于粒子数正好为N的气体。这种推广将薛定谔图像场算符描述为粒子总数的湮灭算符$A$和声子场算符$\chi(X)$之和的乘积，当场算符作用于N个粒子子空间时，声子场算符的形式为$\psi(X)\近似A{\xi(X)+\chi(X)/\Sqrt{N}$。然后可以将哈密顿量展开为Sqrt{N}的递减幂，从而得到本征值和本征态的解作为同类的渐近展开。也可以计算场算符在不同N的状态之间的所有矩阵元素。
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is generalized to apply to a gas with an exact large number $ N$ of particles. This generalization yields a description of the Schr\"odinger picture field operators as the product of an annihilation operator $A$ for the total number of particles and the sum of a ``condensate wavefunction'' $\xi(x)$ and a phonon field operator $\chi(x)$ in the form $\psi(x) \approx A\{\xi(x) + \chi(x)/\sqrt{N}\}$ when the field operator acts on the N particle subspace. It is then possible to expand the Hamiltonian in decreasing powers of $\sqrt{N}$, an thus obtain solutions for eigenvalues and eigenstates as an asymptotic expansion of the same kind. It is also possible to compute all matrix elements of field operators between states of different N.