The quantum geometric phase as a transformation invariant

Guido Bacciagaluppi

Neither geometric phases nor differences in geometric phases are generally invariant under time-dependent unitary transformations (unlike differences in total phases), in particular under local gauge transformations and Galilei transformations. (This was pointed out originally by Aharonov and Anandan, and in the case of Galilei transformations has recently been shown explicitly by Sjoeqvist, Brown and Carlsen.) In this paper, I introduce a phase, related to the standard geometric phase, for which phase differences are both gauge- and Galilei-invariant, and, indeed, invariant under transformations to linearly accelerated coordinate systems. I discuss in what sense this phase can also be viewed as geometric, what its relation is to earlier proposals for making geometric phases invariant under gauge or Galilei transformations, and what is its classical analogue. I finally apply this invariant phase to Berry's derivation of the Aharonov-Bohm effect.

J H Hannay

Zheng Ying-Hong, Tong Chen, Ping Wang +2 more

Properties of geometric phase under Galilean transformation are investigated within a general framework. We found that the geometric phase in the system commonly met with in the laboratory is Galilean invariant. However, this is not always true for general non-relativistic quantum systems. The physical origins of the frame dependence of geometric phase is discussed in detail. We emphasize that the change of geometric phase caused by Galilean boosts does not destroy the results of measurement for two-state interference. It is consistent with the general constraint of Galilean invariance on a non-relativistic quantum system.

Arno Böhm

Nikola Burić, Milan Radonjić

Quantum state diffusion unraveling of the Linblad master equation is utilized to define a geometric phase of an open quantum system.It is then shown that such geometric phase is invariant under unitary symmetry transformations of the Linblad equation, which is important property not shared by the geometric phases based on other types of unraveling.

Arno Böhm, Ali Mostafazadeh, Hiroyasu Koizumi +2 more