Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

Assessing resilience and state-transition models with historical records of cheatgrass Bromus tectorum invasion in North American sagebrush-steppe

1. Resilience-based approaches are increasingly being called upon to inform ecosystem management, particularly in arid and semi-arid regions. This requires management frameworks that can assess ecosystem dynamics, both within and between alternative states, at relevant time scales. 2. We analysed long-term vegetation records from two representative sites in the North American sagebrush-steppe ecosystem, spanning nine decades, to determine if empirical patterns were consistent with resilience theory, and to determine if cheatgrass Bromus tectorum invasion led to thresholds as currently envisioned by expert-based state-and-transition models (STM). These data span the entire history of cheatgrass invasion at these sites and provide a unique opportunity to assess the impacts of biotic invasion on ecosystem resilience. 3. We used univariate and multivariate statistical tools to identify unique plant communities and document the magnitude, frequency and directionality of community transitions through time. Community transitions were characterized by 37-47% dissimilarity in species composition, they were not evenly distributed through time, their frequency was not correlated with precipitation, and they could not be readily attributed to fire or grazing. Instead, at both sites, the majority of community transitions occurred within an 8-10year period of increasing cheatgrass density, became infrequent after cheatgrass density peaked, and thereafter transition frequency declined. 4. Greater cheatgrass density, replacement of native species and indication of asymmetry in community transitions suggest that thresholds may have been exceeded in response to cheatgrass invasion at one site (more arid), but not at the other site (less arid). Asymmetry in the direction of community transitions also identified communities that were at-risk' of cheatgrass invasion, as well as potential restoration pathways for recovery of pre-invasion states. 5. Synthesis and applications. These results illustrate the complexities associated with threshold identification, and indicate that criteria describing the frequency, magnitude, directionality and temporal scale of community transitions may provide greater insight into resilience theory and its application for ecosystem management. These criteria are likely to vary across biogeographic regions that are susceptible to cheatgrass invasion, and necessitate more in-depth assessments of thresholds and alternative states, than currently available.

Supplier selection based on supply chain ecosystem, performance and risk criteria

A supply chain ecosystem consists of the elements of the supply chain and the entities that influence the goods, information and financial flows through the supply chain. These influences come through government regulations, human, financial and natural resources, logistics infrastructure and management, etc., and thus affect the supply chain performance. Similarly, all the ecosystem elements also contribute to the risk. The aim of this paper is to identify both performances-based and risk-based decision criteria, which are important and critical to the supply chain. A two step approach using fuzzy AHP and fuzzy technique for order of preference by similarity to ideal solution has been proposed for multi-criteria decision-making and illustrated using a numerical example. The first step does the selection without considering risks and then in the next step suppliers are ranked according to their risk profiles. Later, the two ranks are consolidated into one. In subsequent section, the method is also extended for multi-tier supplier selection. In short, we are presenting a method for the design of a resilient supply chain, in this paper.

Observation of localized states in atomically thin MoS2 field effect transistor

We present electrical transport arid low frequency (1/f) noise measurements on mechanically exfoliated single, In and triLayer MoS2-based FPI devices on Si/SiO2 substrate. We find that tie electronic states hi MoS2 are localized at low temperatures (T) and conduction happens through variable range hopping (VRH). A steep increase of 1/f noise with decreasing T, typical for localized regime was observed in all of our devices. From gate voltage dependence of noise, we find that the noise power is inversely proportional to square of the number density (proportional to 1/n(2)) for a wide range of T, indicating number density fluctuations to be the dominant source of 1/f noise in these MoS2 FETs.

Exact Solution of the PPP Model for Correlated Electronic States of Tetracene and Substituted Tetracene

Tetracene is an important conjugated molecule for device applications. We have used the diagrammatic valence bond method to obtain the desired states, in a Hilbert space of about 450 million singlets and 902 million triplets. We have also studied the donor/acceptor (D/A)-substituted tetracenes with D and A groups placed symmetrically about the long axis of the molecule. In these cases, by exploiting a new symmetry, which is a combination of C-2 symmetry and electron-hole symmetry, we are able to obtain their low-lying states. In the case of substituted tetracene, we find that optically allowed one-photon excitation gaps reduce with increasing D/A strength, while the lowest singlet triplet gap is only wealdy affected. In all the systems we have studied, the excited singlet state, S-i, is at more than twice the energy of the lowest triplet state and the second triplet is very close to the S-1 state. Thus, donor-acceptor-substituted tetracene could be a good candidate in photovoltaic device application as it satisfies energy criteria for singlet fission. We have also obtained the model exact second harmonic generation (SHG) coefficients using the correction vector method, and we find that the SHG responses increase with the increase in D/A strength.

Comprehensive seismic hazard assessment of Tripura and Mizoram states

Northeast India is one of the most highly seismically active regions in the world with more than seven earthquakes on an average per year of magnitude 5.0 and above. Reliable seismic hazard assessment could provide the necessary design inputs for earthquake resistant design of structures in this' region. In this study, deterministic as well as probabilistic methods have been attempted for seismic hazard assessment of Tripura and Mizoram states at bedrock level condition. An updated earthquake catalogue was collected from various national and international seismological agencies for the period from 1731 to 2011. The homogenization, declustering and data completeness analysis of events have been carried out before hazard evaluation. Seismicity parameters have been estimated using G R relationship for each source zone. Based on the seismicity, tectonic features and fault rupture mechanism, this region was divided into six major subzones. Region specific correlations were used for magnitude conversion for homogenization of earthquake size. Ground motion equations (Atkinson and Boore 2003; Gupta 2010) were validated with the observed PGA (peak ground acceleration) values before use in the hazard evaluation. In this study, the hazard is estimated using linear sources, identified in and around the study area. Results are presented in the form of PGA using both DSHA (deterministic seismic hazard analysis) and PSHA (probabilistic seismic hazard analysis) with 2 and 10% probability of exceedance in 50 years, and spectral acceleration (T = 0. 2 s, 1.0 s) for both the states (2% probability of exceedance in 50 years). The results are important to provide inputs for planning risk reduction strategies, for developing risk acceptance criteria and financial analysis for possible damages in the study area with a comprehensive analysis and higher resolution hazard mapping.

Edge states of a three-dimensional topological insulator

We use the bulk Hamiltonian for a three-dimensional topological insulator such as Bi-2 Se-3 to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states.

Optical properties of an inhomogeneously broadened Lambda V-system with multiple excited states

We present a theoretical model using a density matrix approach to show the influence of multiple excited states on the optical properties of an inhomogeneously broadened Lambda V-system of the Rb-87 D2 line. These closely spaced multiple excited states cause asymmetry in absorption and dispersion profiles. We observe the reduced absorption profiles, due to dressed state interactions of the applied electromagnetic fields, which results the Mollow sideband-like transparency windows. In a room temperature vapor, we obtain a narrow enhanced absorption and steep positive dispersion at the line center when the strengths of control and pump fields are equal. Here, we show how the probe transmittance varies when it passes through the atomic medium. We also discuss the transient behavior of our system which agrees well with the corresponding absorption and dispersion profiles. This study has potential applications in controllability of group velocity, and for optical and quantum information processing.

Glass, Gel, and Liquid Crystals: Arrested States of Graphene Oxide Aqueous Dispersions

Colloidal systems with competing interactions are known to exhibit a range of dynamically arrested states because of the systems' inability to reach its underlying equilibrium state due to intrinsic frustration. Graphene oxide (GO) aqueous dispersions constitute a class of 2D-anisotropic colloids with competing interactions long-range electrostatic repulsion, originating from ionized groups located on the rim of the sheets, and weak dispersive attractive interactions originating from the unoxidized graphitic domains. We show here that aqueous dispersions of GO exhibit a range of arrested states, encompassing fluid, glass, and gels that coexist with liquid-crystalline order with increasing volume fraction. These states can be accessed by varying the relative magnitudes of the repulsive and attractive forces. This can be realized by changing the ionic strength of the medium. We observe at low salt concentrations, where long-range electrostatic repulsion dominates, the formation of a repulsive Wigner glass, while at high salt concentrations, when attractive forces dominate, the formation of gels exhibits a nematic to columnar liquid-crystalline transition. The present work highlights how the chemical structure of GO hydrophilic ionizable groups and hydrophobic graphitic domains coexisting on a single sheet gives rise to a rich and complex array of arrested states.

High-conductance states and A-type K+ channels are potential regulators of the conductance-current balance triggered by HCN channels

An increase in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channel conductance reduces input resistance, whereas the consequent increase in the inward h current depolarizes the membrane. This results in a delicate and unique conductance-current balance triggered by the expression of HCN channels. In this study, we employ experimentally constrained, morphologically realistic, conductance-based models of hippocampal neurons to explore certain aspects of this conductance-current balance. First, we found that the inclusion of an experimentally determined gradient in A-type K+ conductance, but not in M-type K+ conductance, tilts the HCN conductance-current balance heavily in favor of conductance, thereby exerting an overall restorative influence on neural excitability. Next, motivated by the well-established modulation of neuronal excitability by synaptically driven high-conductance states observed under in vivo conditions, we inserted thousands of excitatory and inhibitory synapses with different somatodendritic distributions. We measured the efficacy of HCN channels, independently and in conjunction with other channels, in altering resting membrane potential (RMP) and input resistance (R-in) when the neuron received randomized or rhythmic synaptic bombardments through variable numbers of synaptic inputs. We found that the impact of HCN channels on average RMP, R in, firing frequency, and peak-to-peak voltage response was severely weakened under high-conductance states, with the impinging synaptic drive playing a dominant role in regulating these measurements. Our results suggest that the debate on the role of HCN channels in altering excitability should encompass physiological and pathophysiological neuronal states under in vivo conditions and the spatiotemporal interactions of HCN channels with other channels.

Stress states in individual Si particles of a cast Al-Si alloy: Micro-Raman analysis and microstructure based modeling

The stress states in Si particles of cast Al-Si based alloys depend on its morphology and the heat treatment given to the alloy. The Si particles fracture less on modification and fracture more in the heat treated condition. An attempt has been made in this work to study the effect of heat treatment and Si modification on the stress states of the particles. Such understanding will be valuable for predicting the ductility of the alloy. The stress states of Si particles are estimated by Raman technique and compared with the microstructure-based FEM simulations. Combination of Electron Back-Scattered Diffraction (EBSD) and frequency shift, polarized micro-Raman technique is applied to determine the stress states in Si particles with (111) orientations. Stress states are measured in the as-received state and under uniaxial compression. The residual stress, the stress in the elastic-plastic regime and the stress which causes fracture of the particles is estimated by Raman technique. FEM study demonstrates that the stress distribution is uniform in modified Si, whereas the unmodified Si shows higher and more complex stress states. The onset of plastic flow is observed at sharp corners of the particles and is followed by localization of strain between particles. Clustering of particles generates more inhomogeneous plastic strain in the matrix. Particle stress estimated by Raman technique is in agreement with FEM calculations. (C) 2014 Elsevier B.V. All rights reserved.

A Gaussian network model study suggests that structural fluctuations are higher for inactive states than active states of protein kinases

We performed Gaussian network model based normal mode analysis of 3-dimensional structures of multiple active and inactive forms of protein kinases. In 14 different kinases, a more number of residues (1095) show higher structural fluctuations in inactive states than those in active states (525), suggesting that, in general, mobility of inactive states is higher than active states. This statistically significant difference is consistent with higher crystallographic B-factors and conformational energies for inactive than active states, suggesting lower stability of inactive forms. Only a small number of inactive conformations with the DFG motif in the ``in'' state were found to have fluctuation magnitudes comparable to the active conformation. Therefore our study reports for the first time, intrinsic higher structural fluctuation for almost all inactive conformations compared to the active forms. Regions with higher fluctuations in the inactive states are often localized to the aC-helix, aG-helix and activation loop which are involved in the regulation and/or in structural transitions between active and inactive states. Further analysis of 476 kinase structures involved in interactions with another domain/protein showed that many of the regions with higher inactive-state fluctuation correspond to contact interfaces. We also performed extensive GNM analysis of (i) insulin receptor kinase bound to another protein and (ii) holo and apo forms of active and inactive conformations followed by multi-factor analysis of variance. We conclude that binding of small molecules or other domains/proteins reduce the extent of fluctuation irrespective of active or inactive forms. Finally, we show that the perceived fluctuations serve as a useful input to predict the functional state of a kinase.

Tailoring local density of optical states to control emission intensity and anisotropy of quantum dots in hybrid photonic-plasmonic templates

We report results of controlled tuning of the local density of states (LDOS) in versatile, flexible, and hierarchical self assembled plasmonic templates. Using 5 nm diameter gold (Au) spherical nanoantenna within a polymer template randomly dispersed with quantum dots, we show how the photoluminescence intensity and lifetime anisotropy of these dots can be significantly enhanced through LDOS tuning. Finite difference time domain simulations corroborate the experimental observations and extend the regime of enhancement to a wider range of geometric and spectral parameters bringing out the versatility of these functional plasmonic templates. It is also demonstrated how the templates act as plasmonic resonators for effectively engineer giant enhancement of the scattering efficiency of these nano antenna embedded in the templates. Our work provides an alternative method to achieve spontaneous emission intensity and anisotropy enhancement with true nanoscale plasmon resonators. (C) 2015 AIP Publishing LLC.

Redox-Active Metal-Organic Frameworks: Highly Stable Charge-Separated States through Strut/Guest-to-Strut Electron Transfer

Molecular organization of donor and acceptor chromophores in self-assembled materials is of paramount interest in the field of photovoltaics or mimicry of natural light-harvesting systems. With this in mind, a redox-active porous interpenetrated metal-organic framework (MOF), {Cd(bpdc)(bpNDI)]4.5H(2)ODMF}(n) (1) has been constructed from a mixed chromophoric system. The -oxo-bridged secondary building unit, {Cd-2(-OCO)(2)}, guides the parallel alignment of bpNDI (N,N-di(4-pyridyl)-1,4,5,8-naphthalenediimide) acceptor linkers, which are tethered with bpdc (bpdcH(2)=4,4-biphenyldicarboxylic acid) linkers of another entangled net in the framework, resulting in photochromic behaviour through inter-net electron transfer. Encapsulation of electron-donating aromatic molecules in the electron-deficient channels of 1 leads to a perfect donor-acceptor co-facial organization, resulting in long-lived charge-separated states of bpNDI. Furthermore, 1 and guest encapsulated species are characterised through electrochemical studies for understanding of their redox properties.

Fermionic edge states and new physics

We investigate the properties of the Dirac operator on manifolds with boundaries in the presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.