论文标题
多体动力学与时间相关的相互作用
Many-body Dynamics with Time-dependent Interaction
论文作者
论文摘要
光学Feshbach共振技术的最新进展使原子气体与时间依赖性相互作用进行了实验研究。在这项工作中，我们研究了弱相互作用的玻色子的多体动力学受试者，任意时间变化的散射长度。通过采用变异的ANSATZ，我们得出了一个有效的哈密顿量，该哈密顿量控制热颗粒的动力学。至关重要的是，我们表明，在这个哈密顿量中存在隐藏的对称性，可以将多体动力学映射到SU（1,1）“旋转”的动力上。作为演示，我们计算了散射长度是正弦调制的情况。我们表明，SU（1,1）组的非紧密度自然会导致Bogoliubov模式成倍增长的解决方案，并导致不稳定性。
Recent advances in optical Feshbach resonance technique have enabled the experimental investigation of atomic gases with time-dependent interaction. In this work, we study the many-body dynamics of weakly interacting bosons subject with an arbitrary time varying scattering length. By employing a variational ansatz, we derive an effective Hamiltonian that governs the dynamics of thermal particles. Crucially, we show that there exists a hidden symmetry in this Hamiltonian that can map the many-body dynamics to the precession of an SU(1,1) "spin". As a demonstration, we calculate the situation where the scattering length is sinusoidally modulated. We show that the non-compactness of the SU(1,1) group naturally leads to solutions with exponentially growth of Bogoliubov modes and causes instabilities.
