Numerical Investigation of Time-Evolution of Quantum Wavepacket States in Equilateral Triangular Billiards

Kuan-Yen Chou^1*, Chi-Wei Huang¹, Pi-Hui Tuan¹

¹Department of Physics, National Chung Cheng University, Chiayi, Taiwan

* Presenter:Kuan-Yen Chou, email:tony991026@gmail.com

Quantum billiards studies the dynamical behavior of particle-like quantum states evolving in an energy-conserved two-dimensional enclosure as time varies. In this work, Gaussian wavepacket states by coherent superposition of eigenstates are constructed inside an equilateral triangular billiards to explore the corresponding dynamical behavior of the system. Under appropriate setting of initial conditions, the constructed Gaussian wave packet can mimic a finite-size classical particle moving along the periodic orbit of the billiards. However, unlike classical rigid-body particles, Gaussian wave packet states undergo dispersion and revival of probability density during time-evolution due to the cyclic phase relation between the superposed eigenstates with a finite bandwidth energy spectrum. To clearly unveil the rich spatiotemporal structures of wavepacket states inside the billiards, the quantum carpet is woven by extracting the probability density on the periodic orbit swept by the wave packet. Compared with the autocorrelation function, quantum carpets can not only reflect the fractional revival but also simultaneously offer information about the locality of quantum states which is useful for better understanding the dynamical characteristics of the system.

Keywords: Quantum-classical correspondence, Equilateral triangular billiards, Quantum wavepacket state, Spatiotemporal dynamics, Quantum carpet