Quantum mechanics and Dynamical Systems

Can we study a quintessential quantum phenomenon—such as tunneling—by analyzing dynamical equations of the moments of the quantum distribution?

Recommended

Ballentine, L. E., & McRae, S. M. (1998). Moment equations for probability distributions in classical and quantum mechanics. Physical Review A, 58(3), 1799–1809.

Wheeler, N. (1998). Remarks Concerning the Status & Some Ramifications of Ehrenfest’s Theorem. PDF

Neat. Also see other notes by Wheeler. (This is not John, but Nicholas Wheeler. A colleague of David Griffiths at the Reed college)

Biswas, S., Chattopadhyay, R., & Bhattacharjee, J. K. (2018). Propagation of arbitrary initial wave packets in a quantum parametric oscillator: Instability zones for higher order moments. Physics Letters A, 382(18), 1202–1206

Chawla, R., & Bhattacharjee, J. K. (2019). Quantum dynamics from fixed points and their stability. European Physical Journal B, 92(9), 196.

Sarkar, P., & Bhattacharjee, J. K. (2020). Nonlinear parametric oscillator: A tool for probing quantum fluctuations. Physics Review E, 102(5), 052204.

Ray, S., Bhattacharyya, S., & Bhattacharjee, J. K. (2024). Dynamical System Description of Quantum Tunneling in a Double Well Potential. Physics Letters A, 130174.

Sarkar, P., Chattopadhyay, R., & Bhattacharjee, J. K. (2024). Quantum dynamics of wave packets in a Morse potential: A dynamical system approach. Physical Review E, 110(3), 034207.