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

TL;DR

This paper demonstrates the emergence of Berry phase in a quantum space-time setting using a time-dependent harmonic oscillator model, revealing geometric phase effects due to quantum space-time structure.

Contribution

It introduces a model of a harmonic oscillator in quantum space-time with operator-valued time, deriving geometric phase effects in this novel context.

Findings

Berry phase appears in quantum space-time models

Effective description yields a time-dependent generalized harmonic oscillator

Adiabatic evolution leads to a calculable geometric phase-shift

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.