Boson condensation and instability in the tensor network representation of string-net states

The tensor network representation of many-body quantum states, given by local tensors, provides a promising numerical tool for the study of strongly correlated topological phases in two dimension. However, tensor network representations may be vulnerable to instabilities caused by small perturbations of the local tensor, especially when the local tensor is not injective. For example, the topological order in tensor network representations of the toric code ground state has been shown to be unstable under certain small variations of the local tensor, if these small variations do not obey a local $Z_2$ symmetry of the tensor. In this paper, we ask the questions of whether other types of topological orders suffer from similar kinds of instability and if so, what is the underlying physical mechanism and whether we can protect the order by enforcing certain symmetries on the tensor. We answer these questions by showing that the tensor network representation of all string-net models are indeed unstable, but the matrix product operator (MPO) symmetries of the local tensor can help to protect the order. We find that, `stand-alone' variations that break the MPO symmetries lead to instability because they induce the condensation of bosonic quasi-particles and destroy the topological order in the system. Therefore, such variations must be forbidden for the encoded topological order to be reliably extracted from the local tensor. On the other hand, if a tensor network based variational algorithm is used to simulate the phase transition due to boson condensation, then such variation directions must be allowed in order to access the continuous phase transition process correctly.Comment: 44 pages, 85 figures, comments welcom

Exploring the missing link among d-separable, d¯-separable and d-disjunct matrices

Abstractd-Disjunct matrices, d¯-separable matrices and d-separable matrices are well studied in various problems including group testing, coding, extremal set theory and, recently, DNA sequencing. The implications from the first two matrices to the last one are well documented. This paper gives an implication of the other direction for the first time

Nonequilibrium Ablation of Phenolic Impregnated Carbon Ablator

In previous work, an equilibrium ablation and thermal response model for Phenolic Impregnated Carbon Ablator was developed. In general, over a wide range of test conditions, model predictions compared well with arcjet data for surface recession, surface temperature, in-depth temperature at multiple thermocouples, and char depth. In this work, additional arcjet tests were conducted at stagnation conditions down to 40 W/sq cm and 1.6 kPa. The new data suggest that nonequilibrium effects become important for ablation predictions at heat flux or pressure below about 80 W/sq cm or 10 kPa, respectively. Modifications to the ablation model to account for nonequilibrium effects are investigated. Predictions of the equilibrium and nonequilibrium models are compared with the arcjet data

Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space our results cover the full range of the exponent $s \in (0,1)$ of the fractional Laplacians. We answer in particular an open problem raised by Frank and Seiringer \cite{FS}.Comment: 42 page

Planar Metamaterials for Antireflection Coating

We present a novel antireflection approach utilizing planar metamaterials on dielectric surfaces. It consists of a split-ring resonator array and a metal mesh separated by a thin dielectric spacer. The coating dramatically reduces the reflectance and greatly enhances the transmittance over a wide range of incidence angles and a narrow bandwidth. Antireflection is achieved by tailoring the magnitude and phase shifts of waves reflected and transmitted at metamaterial boundaries, resulting in a destructive interference in reflection and constructive interference in transmission. The coating can be very thin and there is no requirement for the spacer dielectric constant

b -> s gamma in the left-right supersymmetric model

The rare decay $b \to s \gamma$ is studied in the left-right supersymmetric model. We give explicit expressions for all the amplitudes associated with the supersymmetric contributions coming from gluinos, charginos and neutralinos in the model to one-loop level. The branching ratio is enhanced significantly compared to the standard model and minimal supersymmetric standard model values by contributions from the right-handed gaugino and squark sector. We give numerical results coming from the leading order contributions. If the only source of flavor violation comes from the CKM matrix, we constrain the scalar fermion-gaugino sector. If intergenerational mixings are allowed in the squark mass matrix, we constrain such supersymmetric sources of flavor violation. The decay $b \to s \gamma$ sets constraints on the parameters of the model and provides distinguishing signs from other supersymmetric scenarios.Comment: 12 figure

Electromagnetic modes of Maxwell fisheye lens

We provide an analysis of the radial structure of TE and TM modes of the Maxwell fisheye lens, by means of Maxwell equations as applied to the fisheye case. Choosing a lens of size R = 1 cm, we plot some of the modes in the infrared range.Comment: 2+6 pages in Latex, 3 figures to be found in the published referenc