Time-Explicit Simulation of Wave Interaction in Optical Waveguide Crossings at Large Angles

The time-explicit finite-difference time-domain method is used to simulate wave interaction in optical waveguide crossings at large angles. The wave propagation at the intersecting structure is simulated by time stepping the discretized form of the Maxwell’s time dependent curl equations. The power distribution characteristics of the intersections are obtained by extracting the guided-mode amplitudes from these simulated total field data. A physical picture of power flow in the intersection is also obtained from the total field solution; this provides insights into the switching behavior and the origin of the radiations

Matrix Product Representation of Locality Preserving Unitaries

The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that are unitary provides a necessary and sufficient representation of 1D unitaries that preserve locality. That is, we show that matrix product operators that are unitary are guaranteed to preserve locality by mapping local operators to local operators while at the same time all locality preserving unitaries can be represented in a matrix product way. Moreover, we show that the matrix product representation gives a straight-forward way to extract the GNVW index defined in Ref.\cite{Gross2012} for classifying 1D locality preserving unitaries. The key to our discussion is a set of `fixed point' conditions which characterize the form of the matrix product unitary operators after blocking sites. Finally, we show that if the unitary condition is relaxed and only required for certain system sizes, the matrix product operator formalism allows more possibilities than locality preserving unitaries. In particular, we give an example of a simple matrix product operator which is unitary only for odd system sizes, does not preserve locality and carries a `fractional' index as compared to their locality preserving counterparts.Comment: 14 page

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

Investigation of interface properties of sputter deposited TiN/CrN superlattices by low-angle X-ray reflectivity

Approximately 1.8 m thick nanolayered multilayer coatings of TiN/CrN (also known as superlattices) were deposited on silicon (100) substrates at different modulation wavelengths (4.6–12.8 nm), substrate temperatures (50-400 °C) and substrate bias voltages (-50 to -200 V) using a reactive direct current magnetron sputtering system. X-ray reflectivity (XRR) technique was employed to determine various properties of the multilayers such as interface roughness, surface roughness, electron density, critical angle and individual layer thicknesses. The modulation wavelengths of the TiN/CrN superlattice coatings were calculated using modified Bragg’s law. Furthermore, the experimental X-ray reflectivity patterns were simulated using theoretically generated patterns and a good fit was obtained for a three layer model, i.e., (1) top surface roughness layer, (2) TiN/CrN multilayer coating (approximately 1.8 m) and (3) Ti interlayer (~ 0.5 m) at the film-substrate interface. For the superlattice coatings prepared at a modulation wavelength of 9.7 nm, a substrate bias of -200 V and a substrate temperature of 400 C the XRR patterns showed Bragg reflections up to 5th order, indicating well-defined periodicity of the constituent layers and relatively sharp interfaces. The simulation showed that the superlattice coatings prepared under the above conditions exhibited low surface and interface roughnesses. We also present the effect of substrate temperature and substrate bias, which are critical parameters for controlling the superlattice properties, onto the various interface properties of TiN/CrN superlattices

Giant intra-abdominal hydatid cysts with multivisceral locations

The disseminated intra-peritoneal hydatid disease is a very rare finding. A case of disseminated intra abdominal hydatid disease is presented along with a review of literature and various therapeutic modalitie

Physical Learning Environment Challenges in the Digital Divide: How to Design Effective Instruction during COVID-19?

The coronavirus disease of 2019 (COVID-19) pandemic has changed the way we work, learn, and interact with others in society. Academic institutions have responded to the pandemic by shifting face-to-face teaching to online instruction. However, whether online instruction succeeds also depends on students’ social and physical learning environment, particularly in developing countries. In this paper, we discuss how learning space challenges exacerbate the digital divide. We argue that weak digital infrastructure, combined with family and social dynamics, create learning space inequality that negatively influence learning outcomes. We provide recommendations on how academic institutions can reimagine content delivery, evaluation, and student support to mitigate learning space inequalities