Time-dependent Aharonov-Bohm effect on the noncommutative space

We study the time-dependent Aharonov-Bohm effect on the noncommutative space. Because there is no net Aharonov-Bohm phase shift in the time-dependent case on the commutative space, therefore, a tiny deviation from zero indicates new physics. Based on the Seiberg-Witten map we obtain the gauge invariant and Lorentz covariant Aharonov-Bohm phase shift in general case on noncommutative space. We find there are two kinds of contribution: momentum-dependent and momentum-independent corrections. For the momentum-dependent correction, there is a cancellation between the magnetic and electric phase shifts, just like the case on the commutative space. However, there is a non-trivial contribution in the momentum-independent correction. This is true for both the time-independent and time-dependent Aharonov-Bohm effects on the noncommutative space. However, for the time-dependent Aharonov-Bohm effect, there is no overwhelming background which exists in the time-independent Aharonov-Bohm effect on both commutative and noncommutative space. Therefore, the time-dependent Aharonov-Bohm can be sensitive to the spatial noncommutativity. \draftnote{The net correction is proportional to the product of the magnetic fluxes through the fundamental area represented by the noncommutative parameter $\theta$, and through the surface enclosed by the trajectory of charged particle.} More interestingly, there is an anti-collinear relation between the logarithms of the magnetic field $B$ and the averaged flux $\Phi/N$ (N is the number of fringes shifted). This nontrivial relation can also provide a way to test the spatial noncommutativity. For $B\Phi/N\sim 1$, our estimation on the experimental sensitivity shows that it can reach the $\rm 10GeV$ scale. This sensitivity can be enhanced by using stronger magnetic field strength, larger magnetic flux, as well as higher experimental precision on the phase shift.Comment: 12 pages, 1 figure; v2, accepted version by PL

The one-dimensional polymer poly[[aqua­(2,2′-bipyridine)cadmium(II)]-μ-trans-stilbene-4,4′-dicarboxyl­ato]

In the title polymer, [Cd(C16H10O4)(C10H8N2)(H2O)]n, the CdII ion is in a strongly distorted octa­hedral geometry, being coordinated by two N atoms from a 2,2′-bipyridine ligand, three carboxylate O atoms from two symmetry-related trans-stilbene-4,4′-dicarboxyl­ate dianions and one water mol­ecule. The stilbene ligand lies on an inversion centre at the midpoint of the central C=C bond. This feature generates the polymeric structure: adjacent CdII ions are bridged by trans-stilbene-4,4′-dicarboxyl­ate dianions, giving rise to a one-dimensional structure. The coordinated water mol­ecule is involved in interchain O—H⋯O hydrogen bonds