Lorentz violation dispersion relation and its application

We derive a modified dispersion relation (MDR) in the Lorentz violation extension of quantum electrodynamics (QED) sector in the standard model extension (SME) framework. Based on the extended Dirac equation and corresponding MDR, we observe the resemblance of the Lorentz violation coupling with spin-gravity coupling. We also develop a neutrino oscillation mechanism induced by the presence of nondiagonal terms of Lorentz violation couplings in 2-flavor space in a 2-spinor formalism by explicitly assuming neutrinos to be Marjorana fermions. We also obtain a much stringent bound ($\backsim10^{-25}$) on one of the Lorentz violation parameters by applying MDR to the ultrahigh energy cosmic ray (UHECR) problem.Comment: 22 Latex pages, final version in publicatio

Competition between Phase Separation and Spin Density Wave or Charge Density Wave Order: Role of Long-Range Interactions

Recent studies of pairing and charge order in materials such as FeSe, SrTiO$_3$, and 2H-NbSe$_2$ have suggested that momentum dependence of the electron-phonon coupling plays an important role in their properties. Initial attempts to study Hamiltonians which either do not include or else truncate the range of Coulomb repulsion have noted that the resulting spatial non-locality of the electron-phonon interaction leads to a dominant tendency to phase separation. Here we present Quantum Monte Carlo results for such models in which we incorporate both on-site and intersite electron-electron interactions. We show that these can stabilize phases in which the density is homogeneous and determine the associated phase boundaries. As a consequence, the physics of momentum dependent electron-phonon coupling can be determined outside of the trivial phase separated regime.Comment: 9 pages, 7 figure

Evaluating probability forecasts

Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used to assess the efficacy of the forecast probabilities after observing the occurrence, or nonoccurrence, of the predicted events. We develop herein a statistical theory for scoring rules and propose an alternative approach to the evaluation of probability forecasts. This approach uses loss functions relating the predicted to the actual probabilities of the events and applies martingale theory to exploit the temporal structure between the forecast and the subsequent occurrence or nonoccurrence of the event.Comment: Published in at http://dx.doi.org/10.1214/11-AOS902 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Unexpected Accumulation of ncm\u3csup\u3e5\u3c/sup\u3eU and ncm\u3csup\u3e5\u3c/sup\u3es\u3csup\u3e2\u3c/sup\u3eU in a \u3cem\u3etrm9\u3c/em\u3e Mutant Suggests an Additional Step in the Synthesis of mcm\u3csup\u3e5\u3c/sup\u3eU and mcm\u3csup\u3e5\u3c/sup\u3es\u3csup\u3e2\u3c/sup\u3eU

Background Transfer RNAs are synthesized as a primary transcript that is processed to produce a mature tRNA. As part of the maturation process, a subset of the nucleosides are modified. Modifications in the anticodon region often modulate the decoding ability of the tRNA. At position 34, the majority of yeast cytosolic tRNA species that have a uridine are modified to 5-carbamoylmethyluridine (ncm5U), 5-carbamoylmethyl-2′-O-methyluridine (ncm5Um), 5-methoxycarbonylmethyl-uridine (mcm5U) or 5-methoxycarbonylmethyl-2-thiouridine (mcm5s2U). The formation of mcm5 and ncm5 side chains involves a complex pathway, where the last step in formation of mcm5 is a methyl esterification of cm5 dependent on the Trm9 and Trm112 proteins. Methodology and Principal Findings Both Trm9 and Trm112 are required for the last step in formation of mcm5 side chains at wobble uridines. By co-expressing a histidine-tagged Trm9p together with a native Trm112p in E. coli, these two proteins purified as a complex. The presence of Trm112p dramatically improves the methyltransferase activity of Trm9p in vitro. Single tRNA species that normally contain mcm5U or mcm5s2U nucleosides were isolated from trm9Δ or trm112Δ mutants and the presence of modified nucleosides was analyzed by HPLC. In both mutants, mcm5U and mcm5s2U nucleosides are absent in tRNAs and the major intermediates accumulating were ncm5U and ncm5s2U, not the expected cm5U and cm5s2U. Conclusions Trm9p and Trm112p function together at the final step in formation of mcm5U in tRNA by using the intermediate cm5U as a substrate. In tRNA isolated from trm9Δ and trm112Δ strains, ncm5U and ncm5s2U nucleosides accumulate, questioning the order of nucleoside intermediate formation of the mcm5 side chain. We propose two alternative explanations for this observation. One is that the intermediate cm5U is generated from ncm5U by a yet unknown mechanism and the other is that cm5U is formed before ncm5U and mcm5U

Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point

The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al. Nature 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors, i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in non-chiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.Comment: 15 pages, 11 figure