Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase
arXiv:2110.04730 · doi:10.1016/j.nuclphysb.2022.115691
Abstract
We show the emergence of Berry phase in a forced harmonic oscillator system placed in the quantum space-time of Moyal type, where the time 't' is also an operator. An effective commutative description of the system gives a time dependent generalised harmonic oscillator system with perturbation linear in position and momentum. The system is then diagonalised to get a generalised harmonic oscillator and then its adiabatic evolution over time-period is studied in Heisenberg picture to compute the expression of geometric phase-shift.
21 pages, Version 2 contains some correction