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

Multi-channel Encoder for Neural Machine Translation

Attention-based Encoder-Decoder has the effective architecture for neural machine translation (NMT), which typically relies on recurrent neural networks (RNN) to build the blocks that will be lately called by attentive reader during the decoding process. This design of encoder yields relatively uniform composition on source sentence, despite the gating mechanism employed in encoding RNN. On the other hand, we often hope the decoder to take pieces of source sentence at varying levels suiting its own linguistic structure: for example, we may want to take the entity name in its raw form while taking an idiom as a perfectly composed unit. Motivated by this demand, we propose Multi-channel Encoder (MCE), which enhances encoding components with different levels of composition. More specifically, in addition to the hidden state of encoding RNN, MCE takes 1) the original word embedding for raw encoding with no composition, and 2) a particular design of external memory in Neural Turing Machine (NTM) for more complex composition, while all three encoding strategies are properly blended during decoding. Empirical study on Chinese-English translation shows that our model can improve by 6.52 BLEU points upon a strong open source NMT system: DL4MT1. On the WMT14 English- French task, our single shallow system achieves BLEU=38.8, comparable with the state-of-the-art deep models.Comment: Accepted by AAAI-201