动边界一维无限深势阱中粒子的演化

TIME EVOLUTION OF A PARTICLE IN A ONE-DIMENSIONAL INFINITE SQUARE WELL POTENTIAL WITH MOVING BOUNDARY

因其时间上的周期性,周期驱动的量子系统在很多方面都展现出了奇异的物理性质,如绝热演化和时间晶体。在简单物理系统中展示这些奇异性质不仅可以加深对量子力学的理解,还可以培养学生的科研兴趣。本文展示当一维无限深方势阱的边界发生周期变化时,处于势阱中粒子的时间演化规律。研究考虑了绝热演化与非绝热演化两种情况,通过解析分析和数值模拟,求解了绝热和非绝热两种情况下,系统在不同参数以及边界运动模式下基态的占据几率。通过求解系统能量期望值和能量偏离值,给出了边界的振动频率和强度对粒子处于不同能级概率的影响。结果表明:相同速度的势阱扩张和收缩运动对阱中粒子的时间演化影响不同;不同的阱壁周期运动模式对粒子的时间演化影响也不同。本文还对数值方法给出的结果进行了简单的解释。

As a useful tool to manipulate the feature of quantum systems,periodic drive has attracted widespread attention.Various exotic phases and rich dynamics have been found in the periodically driven quantum systems,such as adiabatic evolution and time crystals.Displaying these strange properties in a simple physical system can not only deepen the understanding of quantum mechanics,but also cultivate students'interest in scientific research.Here,we are interested in a specific case that the well-geometry changing is caused by boundary contraction or expansion.The simplest one-dimensional square well with periodically moving boundary is examined.We explore the influence of the frequency and the intensity of the drive on the time evolution of the system.By numerical simulations,we calculate the evolution of the ground state occupation taking two cases under different boundary parameters and moving paths in both adiabatic and non adiabatic cases.By solving the expected value and deviation value of the energyofthesystem,the influence of the vibration frequency and intensity of the boundary on the probability of the particles at different energy levels is given.The results show that the expansion and contraction of the potential well with the same velocity have different effects on the time evolution of the particles in the well;Different well wall periodic motion modes have different effects on the time evolution of particles.The results obtained by the numerical method are also explained in this paper.