Giant enhanced optical nonlinearity of colloidal nanocrystals with a graded-index host

The effective linear and third-order nonlinear optical properties of metallic colloidal crystal immersed in a graded-index host fluid are investigated theoretically. The local electric fields are extracted self-consistently based on the layer-to-layer interactions, which are readily given by the Lekner summation method. The resultant optical absorption and nonlinearity enhancement show a series of sharp peaks, which merge in a broadened resonant band. The sharp peaks become a continuous band for increasing packing density and number of layers. We believe that the sharp peaks arise from the in-plane dipolar interactions and the surface plasmon resonance, whereas the continuous band is due to the presence of the gradient in the host refractive index. These results have not been observed in homogeneous and randomly-dispersed colloids, and thus would be of great interest in optical nanomaterial engineering.Comment: Submitted to Applied Physics Letter

On the number of nonequivalent propelinear extended perfect codes

The paper proves that there exist an exponential number of nonequivalent propelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the properties of these codes and show that any of them has a normalized propelinear representation

Space-time symplectic extension

It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time local structure group. A discrete sequence of the metric space-times of the fixed dimensionalities d=(2l)^2 and signatures, with l(2l-1) time-like and l(2l+1) space-like directions, defined over the set of the Hermitian second-rank spin-tensors is considered as an alternative to the pseudo-Euclidean extra dimensional space-times. The basic concepts of the symplectic framework are developed in general, and the ordinary and next-to-ordinary space-time cases with l=1,2, respectively, are elaborated in more detail. In particular, the scheme provides the rationale for the four-dimensionality and 1+3 signature of the ordinary space-time.Comment: 15 pp, LaTe

On the GBM event seen 0.4 sec after GW 150914

In view of the recent report by Connaughton we analyse continuous TTE data of Fermi-GBM around the time of the gravitational wave event GW 150914. We find that after proper accounting for low count statistics, the GBM transient event at 0.4 s after GW 150914 is likely not due to an astrophysical source, but consistent with a background fluctuation, removing the tension between the INTEGRAL/ACS non-detection and GBM. Additionally, reanalysis of other short GRBs shows that without proper statistical modeling the fluence of faint events is over-predicted, as verified for some joint GBM-ACS detections of short GRBs. We detail the statistical procedure to correct these biases. As a result, faint short GRBs, verified by ACS detections, with significances in the broad-band light curve even smaller than that of the GBM-GW150914 event are recovered as proper non-zero source, while the GBM-GW150914 event is consistent with zero fluence.Comment: 13 pages, 12 figures, ApJL (acc.); subm. 2016 March 10, Apr 21 (1st rev.), May 13 (2nd rev), Jun 1 (3rd rev), and editorial changes by Jun 2 (4th rev), Jun 8 (5th rev): Our manuscript refers exclusively to arXiv:1602.03920.v3 since we had no prior access to arXiv:1602.03920.v4/5 (2016 May 31). Note that JG and HFY are not co-authors on arXiv:1602.03920.v4/

Nonanalyticity of the induced Carroll-Field-Jackiw term at finite temperature

In this paper, we discuss the behavior of the Carroll-Field-Jackiw (CFJ) coefficient $k^{\mu}$ arising due to integration over massive fermions, and the modification suffered by its topological structure in the finite temperature case. Our study is based on the imaginary time formalism and summation over the Matsubara frequencies. We demonstrate that the self-energy of photon is non-analytic for the small $k^{\mu}$ limit, i.e., the static limit $(k_0=0,\vec k\rightarrow 0)$ and the long wavelength limit $(k_0\rightarrow 0,\vec k= 0)$ do not commute, while the tensorial structure of the CFJ term holds in both limits.Comment: 12 pages, 1 figur