The notions of the SMARANDACHE GROUP and the SMARANDACHE BOOLEAN RING

The notions of the Snmarandache group and the Smarandache Boolean ring are introduced here with the help of group action and ring action i.e. module respectively. The centre of the Smarandache groupoid is determined. These are very important for the study of Algebraic structures

D - Form of SMARANDACHE GROUPOID

This article is about D - Form of SMARANDACHE GROUPOID

Photon-induced droplet-like bound states in one-dimensional qubit array

We consider an array of $N_e$ non-interacting qubits or emitters that are coupled to a one-dimensional cavity array with tunneling energy $J$ and non-linearity of strength $U$. The number of cavities is assumed to be larger than the number of qubits. Working in the two-excitation manifold, we focus on the bandgap regime where the energy of two excited qubits is off-resonant with the two-photon bound state band. A two-step adiabatic elimination of the photonic degrees of freedom gives rise to a one-dimensional spin Hamiltonian with effective interactions; specifically, the Hamiltonian features constrained single-qubit hopping and pair hopping interactions not only between nearest neighbors but also between next-to-nearest and next-to-next-to-nearest spins. For a regularly arranged qubit array, we identify parameter combinations for which the system supports novel droplet-like bound states whose characteristics depend critically on the pair hopping. The droplet-like states can be probed dynamically. The bound states identified in our work for off-resonance conditions are distinct from localized hybridized states that emerge for on-resonance conditions.Comment: 13 figure

Evaluation of rice–legume–rice cropping system on grain yield, nutrient uptake, nitrogen fixation, and chemical, physical, and biological properties of soil

To achieve higher yields and better soil quality under rice–legume–rice (RLR) rotation in a rainfed production system, we formulated integrated nutrient management (INM) comprised of Azospirillum (Azo), Rhizobium (Rh), and phosphate-solubilizing bacteria (PSB) with phosphate rock (PR), compost, and muriate of potash (MOP). Performance of bacterial bioinoculants was evaluated by determining grain yield, nitrogenase activity, uptake and balance of N, P, and Zn, changes in water stability and distribution of soil aggregates, soil organic C and pH, fungal/bacterial biomass C ratio, casting activities of earthworms, and bacterial community composition using denaturing gradient gel electrophoresis (DGGE) fingerprinting. The performance comparison was made against the prevailing farmers’ nutrient management practices [N/P2O5/K2O at 40:20:20 kg ha−1 for rice and 20:30:20 kg ha−1 for legume as urea/single super-phosphate/MOP (urea/SSP/MOP)]. Cumulative grain yields of crops increased by 7–16% per RLR rotation and removal of N and P by six crops of 2 years rotation increased significantly (P < 0.05) in bacterial bioinoculants-based INM plots over that in compost alone or urea/SSP/MOP plots. Apparent loss of soil total N and P at 0–15 cm soil depth was minimum and apparent N gain at 15–30 cm depth was maximum in Azo/Rh plus PSB dual INM plots. Zinc uptake by rice crop and diethylenetriaminepentaacetate-extractable Zn content in soil increased significantly (P < 0.05) in bacterial bioinoculants-based INM plots compared to other nutrient management plots. Total organic C content in soil declined at 0–15 cm depth and increased at 15–30 cm depth in all nutrient management plots after a 2-year crop cycle; however, bacterial bioinoculants-based INM plots showed minimum loss and maximum gain of total organic C content in the corresponding soil depths. Water-stable aggregation and distribution of soil aggregates in 53–250- and 250–2,000 μm classes increased significantly (P < 0.05) in bacterial bioinoculants-based INM plots compared to other nutrient management plots. Fungal/bacterial biomass C ratio seems to be a more reliable indicator of C and N dynamics in acidic soils than total microbial biomass C. Compost alone or Azo/Rh plus PSB dual INM plots showed significantly (P < 0.05) higher numbers of earthworms’ casts compared to urea/SSP/MOP alone and bacterial bioinoculants with urea or SSP-applied plots. Hierarchical cluster analysis based on similarity matrix of DGGE profiles revealed changes in bacterial community composition in soils due to differences in nutrient management, and these changes were seen to occur according to the states of C and N dynamics in acidic soil under RLR rotation

Implications of surface noise for the motional coherence of trapped ions

Electric noise from metallic surfaces is a major obstacle towards quantum applications with trapped ions due to motional heating of the ions. Here, we discuss how the same noise source can also lead to pure dephasing of motional quantum states. The mechanism is particularly relevant at small ion-surface distances, thus imposing a new constraint on trap miniaturization. By means of a free induction decay experiment, we measure the dephasing time of the motion of a single ion trapped 50~$\mu$m above a Cu-Al surface. From the dephasing times we extract the integrated noise below the secular frequency of the ion. We find that none of the most commonly discussed surface noise models for ion traps describes both, the observed heating as well as the measured dephasing, satisfactorily. Thus, our measurements provide a benchmark for future models for the electric noise emitted by metallic surfaces.Comment: (5 pages, 4 figures

Scaling of NonOhmic Conduction in Strongly Correlated Systems

A new scaling formalism is used to analyze nonlinear I-V data in the vicinity of metal-insulator transitions (MIT) in five manganite systems. An exponent, called the nonlinearity exponent, and an onset field for nonlinearity, both characteristic of the system under study, are obtained from the analysis. The onset field is found to have an anomalously low value corroborating the theoretically predicted electronically soft phases. The scaling functions above and below the MIT of a polycrystalline sample are found to be the same but with different exponents which are attributed to the distribution of the MIT temperatures. The applicability of the scaling in manganites underlines the universal response of the disordered systems to electric field