含时弱耦合玻色气体的时间演化及准粒子表象

Time Evolution and Quasi-particle Representation of the Time-dependent Weakly Coupling Bosonic Gas

本文用不变量理论精确求解了弱耦合玻色气体含时Schrodinger方程并研究了其时间演化问题.由于含时系统的Bogoliubov变换会导致弱耦合玻色气体准粒子表象完备基矢组存在无法自定的含时相位因子,本文通过计算玻色气体微扰前粒子数表象与准粒子表象间的变换系数,获得了弱耦合玻色气体准粒子表象的完备基矢组从而解决了这一困难.

The time-dependent Schrodinger equation governing the time-dependent weakly coupling Bosonic gas is exactly solved by use of the Lewis-Riesenfeld invariant theory in the present paper. This enables us to treat the time evolution of the Bosonic gas. Since the Bogoliubov transformation formulation in the time-dependent case may yield a phase factor that cannot be determined by the theory itself, we calculate the transformation coefficients between the Bosonic occupation representation and the quasi-particle representation and, based on this, obtain the complete set of vector basis of the quasi-particle representation for the time-dependent weakly coupling Bosonic gas.