Generalised geometric phase

Vivek M. Vyas

An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum systems. While probing the average of any observable it is found that a quantum system exhibits different ray spaces and associated fibre bundle structures. The generalised geometric phase is understood as (an)holonomy of a connection over these fibre bundles. The underlying ray spaces in general are found to be pseudo-Kahler manifolds, and its symplectic structure gets manifests as the generalised geometric phase.

Péter Lévay

Anwesha Chakraborty, Partha Nandi, Biswajit Chakraborty

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 T is studied in Heisenberg picture to compute the expression of geometric phase-shift.

T. S. Yakovleva, A. M. Rostom, V. A. Tomilin +1 more

Abstract We consider a quantum system subjected to a controlled phase transformation and interaction with the environment in between the acts of selection, which leads to the emergence of interference effects. It is shown that the shift of the dependence of the statistics of contacts’ information with the environement on the controlled phase shift can be interpreted as a geometric phase. This interpretation is consistent with the known operational approach to the geometric phase. As a result, we suggest generalising the operational approach to the realm of pre- and post-selected quantum states.

Jerrold Eldon Marsden