具有时间依赖频率和边界条件的谐振子的非绝热Berry相位

The non-adiabatic Berry Phase of the Quantum State of a Harmonic Oscillator with Time-dependent Frequency and Boundary Conditions

我们表明具有时间依赖的频率和边界条件的谐振子的哈密顿算符同具有一运动阱壁的无限深势阱内粒子的有效哈密顿算符由一含时规范变换相关联,进而我们利用几何距离和曲线的几何长度概念计算该体系量子态的非绝热Berrg相位。

We shown that the Hamiltonian of the harmonic oscillator with time-dependent frequency and boundary conditions is related to the effective Harmiltonian of a particle in an infinite potential well with a moving wall by a time-dependent gauge transformation. Furthermore, we calculated the non-adiabatic Berry phase of wave function of the harmonic oscillator with time-dependent frequency and boundary conditions by using the geometric concepts such as the geometric distance and geometric length of the curve.