Critical level crossings and gapless spin liquid in the square-lattice spin-1/2 J1-J2 Heisenberg antiferromagnet

We use the DMRG method to calculate several energy eigenvalues of the frustrated S = 1 / 2 square-lattice J 1 - J 2 Heisenberg model on 2 L × L cylinders with L ≤ 10. We identify excited-level crossings versus the coupling ratio g = J 2 /J 1 and study their drifts with the system size L . The lowest singlet-triplet and singlet-quintuplet crossings converge rapidly (with corrections ∝ L − 2 ) to different g values, and we argue that these correspond to ground-state transitions between the N ́eel antiferromagnet and a gapless spin liquid, at g c 1 ≈ 0 . 46, and between the spin liquid and a valence-bond-solid at g c 2 ≈ 0 . 52. Previous studies of order parameters were not able to positively discriminate between an extended spin liquid phase and a critical point. We expect level-crossing analysis to be a generically powerful tool in DMRG studies of quantum phase transitions.Accepted manuscrip

Analysis of Power-aware Buffering Schemes in Wireless Sensor Networks

We study the power-aware buffering problem in battery-powered sensor networks, focusing on the fixed-size and fixed-interval buffering schemes. The main motivation is to address the yet poorly understood size variation-induced effect on power-aware buffering schemes. Our theoretical analysis elucidates the fundamental differences between the fixed-size and fixed-interval buffering schemes in the presence of data size variation. It shows that data size variation has detrimental effects on the power expenditure of the fixed-size buffering in general, and reveals that the size variation induced effects can be either mitigated by a positive skewness or promoted by a negative skewness in size distribution. By contrast, the fixed-interval buffering scheme has an obvious advantage of being eminently immune to the data-size variation. Hence the fixed-interval buffering scheme is a risk-averse strategy for its robustness in a variety of operational environments. In addition, based on the fixed-interval buffering scheme, we establish the power consumption relationship between child nodes and parent node in a static data collection tree, and give an in-depth analysis of the impact of child bandwidth distribution on parent's power consumption. This study is of practical significance: it sheds new light on the relationship among power consumption of buffering schemes, power parameters of radio module and memory bank, data arrival rate and data size variation, thereby providing well-informed guidance in determining an optimal buffer size (interval) to maximize the operational lifespan of sensor networks

On l-adic representations for a space of noncongruence cuspforms

This paper is concerned with a compatible family of 4-dimensional \ell-adic representations \rho_{\ell} of G_\Q:=\Gal(\bar \Q/\Q) attached to the space of weight 3 cuspforms S_3 (\Gamma) on a noncongruence subgroup \Gamma \subset \SL. For this representation we prove that: 1.)It is automorphic: the L-function L(s, \rho_{\ell}^{\vee}) agrees with the L-function for an automorphic form for \text{GL}_4(\mathbb A_{\Q}), where \rho_{\ell}^{\vee} is the dual of \rho_{\ell}. 2.) For each prime p \ge 5 there is a basis h_p = \{h_p ^+, h_p ^- \} of S_3 (\Gamma) whose expansion coefficients satisfy 3-term Atkin and Swinnerton-Dyer (ASD) relations, relative to the q-expansion coefficients of a newform f of level 432. The structure of this basis depends on the class of p modulo 12. The key point is that the representation $\rho_{\ell}$ admits a quaternion multiplication structure in the sense of a recent work of Atkin, Li, Liu and Long.Comment: Second revised version. To appear: Proceedings of the American Mathematical Societ

Fate of the Peak Effect in a Type-II Superconductor: Multicriticality in the Bragg-Glass Transition

We have used small-angle-neutron-scattering (SANS) and ac magnetic susceptibility to investigate the global magnetic field H vs temperature T phase diagram of a single crystal Nb in which a first-order transition of Bragg-glass melting (disordering), a peak effect, and surface superconductivity are all observable. It was found that the disappearance of the peak effect is directly related to a multicritical behavior in the Bragg-glass transition. Four characteristic phase boundary lines have been identified on the H-T plane: a first-order line at high fields, a mean-field-like continuous transition line at low fields, and two continuous transition line associated with the onset of surface and bulk superconductivity. All four lines are found to meet at a multicritical point.Comment: 4 figure

A Note on Topological M5-branes and String-Fivebrane Duality

We derive the stability conditions for the M5-brane in topological M-theory using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is necessarily non-vanishing, as is the case also for the 2-form field strengths on coisotropic branes in topological string theory. It is demonstrated that the self-duality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) in G_2. The double dimensional reduction of the M5-brane is the D4-brane, and its direct reduction is an NS5-brane. We show that the equation of motion for the 3-form on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer equation, providing support for a string-fivebrane duality in topological string theory.Comment: 11 pp, plain te

Formation of Non-reciprocal Bands in Magnetized Diatomic Plasmonic Chains

We show that non-reciprocal bands can be formed in a magnetized periodic chain of spherical plasmonic particles with two particles per unit cell. Simplified form of symmetry operators in dipole approximations are used to demonstrate explicitly the relation between spectral non-reciprocity and broken spatial-temporal symmetries. Due to hybridization among plasmon modes and free photon modes, strong spectral non-reciprocity appears in region slightly below the lightline, where highly directed guiding of energy can be supported. The results may provide a clear guidance on the design of one-way waveguides

Quantitative estimates of fish abundance from boat electrofishing

Multiple removals by boat electro-fishing were used to estimate fish populations in non-wadeable habitats in New Zealand lakes and rivers. Mean capture probability was 0.47±h0.10 (± 95% CI) from 35 population estimates made with 2-7 successive removals. The relationship between the population estimate from the Zippin method (Y)and the number of fish caught in the first removal (X) was significant (adjusted r2=0.84, P<0.001; Figure 2). The least-squares regression was Y = 1.55X 1.23. Mean density ± 95% confidence interval for 13 fishing occasions was 30±27 fish 100 m- 2. Mean biomass of fish for sites was 78±39 g m-2 (range 29 to 245 g m-2). Koi carp comprised the largest proportion of the fish biomass wherever they were present. The high biomasses of koi carp estimated in these results (mean 56±33 g m-2) suggest that they can reach problematic abundances in New Zealand. Bioniass of spawning koi carp can exceed 400 g m-2