Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase

• URL: http://arxiv.org/abs/2110.04730v3
• Date: Mon, 21 Feb 2022 14:16:49 GMT
• Title: Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase
• Authors: Anwesha Chakraborty, Partha Nandi, Biswajit Chakraborty
• Abstract summary: We show the emergence of Berry phase in a forced harmonic oscillator system placed in the quantum space-time of Moyal type. Adiabatic evolution over time-period $mathcalT$ is studied in Heisenberg picture to compute the expression of geometric phase-shift.
• Score: 0.9176056742068814
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\mathcal{T}$ is studied in Heisenberg picture to compute the expression of geometric phase-shift.

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