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

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.

arXiv comment21 pages, Version 2 contains some correction

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Cited by in corpus (4)

• Quadratic Time-dependent Quantum Harmonic Oscillator
• Path Integrals from Spacetime Quantum Actions
• Schrödinger from Wheeler-DeWitt: The Issues of Time and Inner Product in Canonical Quantum Gravity
• Diffeomorphism-Invariant Quantities in Phase Space: More than Correlations