Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation eta and eta + d eta, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice.We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation η and η + dη, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary

On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the (z) over cap direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/tau across a quantum critical point, we find that the density of defects thereby produced scales as 1/tau(q/(q+1)), deviating from the 1/root tau scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of tau, although it may exhibit a crossover at intermediate values of tau. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.

Quantum capacitance in bilayer graphene nanoribbon

We address a physically based analytical model of quantum capacitance (C-Q) in a bilayer graphene nanoribbon (BGN) under the application of an external longitudinal static bias. We demonstrate that as the gap (Delta) about the Dirac point increases, a phenomenological population inversion of the carriers in the two sets of subbands occurs. This results in a periodic and composite oscillatory behavior in the C-Q with the channel potential, which also decreases with increase in Delta. We also study the quantum size effects on the C-Q, which signatures heavy spatial oscillations due to the occurrence of van Hove singularities in the total density-of-states function of both the sets of subbands. All the mathematical results as derived in this paper converge to the corresponding well-known solution of graphene under certain limiting conditions and this compatibility is an indirect test of our theoretical formalism. (C) 2012 Elsevier By. All rights reserved.

Search on a fractal lattice using a quantum random walk

The spatial search problem on regular lattice structures in integer number of dimensions d >= 2 has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here, we investigate the spatial search problem on fractals of noninteger dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (and not the fractal) dimension. Our numerical results have been obtained on the well-known Sierpinski gaskets in two and three dimensions.

Evolution of quantum discord and its stability in two-qubit NMR systems

We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.

Charge transport in functionalized multi-wall carbon nanotube-Nafion composite

The charge transport in sulfonated multi-wall carbon nanotube (sMWNT)-Nafion composite is reported. The scanning electron microscope images of the composite, at 1 and 10 wt % of sMWNT, show that the nanotubes are well dispersed in polymer matrix, with conductivity values of 0.005 and 3.2 S/cm, respectively; and the percolation threshold is nearly 0.42 wt. %. The exponent (∼0.25) of the temperature dependence of conductivity in both samples indicates Mott's variable range hopping (VRH) transport. The conductance in 1 wt. % sample increases by three orders of magnitude at high electric-fields, consistent with VRH model. The negative magnetoresistance in 10 wt. % sample is attributed to the forward interference scattering mechanism in VRH transport. The ac conductance in 1 wt. % sample is expressed by σ(ω)∝ωs, and the temperature dependence of s follows the correlated barrier hopping model.

Decentralized linear quadratic power system stabilizers for multi-machine power systems

Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead-lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not available in most of the power plants. Full state feedback controllers require feedback of other machine states in a multi-machine power system and necessitate block diagonal structure constraints for decentralized implementation. This paper investigates the design of Linear Quadratic Power System Stabilizers using a recently proposed modified Heffron-Phillip's model. This model is derived by taking the secondary bus voltage of the step-up transformer as reference instead of the infinite bus. The state variables of this model can be obtained by local measurements. This model allows a coordinated linear quadratic control design in multi machine systems. The performance of the proposed controller has been evaluated on two widely used multi-machine power systems, 4 generator 10 bus and 10 generator 39 bus systems. It has been observed that the performance of the proposed controller is superior to that of the conventional Power System Stabilizers (PSS) over a wide range of operating and system conditions.

Multi-model climate change projections for India under representative concentration pathways

Climate projections for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) are made using the newly developed representative concentration pathways (RCPs) under the Coupled Model Inter-comparison Project 5 (CMIP5). This article provides multi-model and multi-scenario temperature and precipitation projections for India for the period 1860-2099 based on the new climate data. We find that CMIP5 ensemble mean climate is closer to observed climate than any individual model. The key findings of this study are: (i) under the business-as-usual (between RCP6.0 and RCP8.5) scenario, mean warming in India is likely to be in the range 1.7-2 degrees C by 2030s and 3.3-4.8 degrees C by 2080s relative to pre-industrial times; (ii) all-India precipitation under the business-as-usual scenario is projected to increase from 4% to 5% by 2030s and from 6% to 14% towards the end of the century (2080s) compared to the 1961-1990 baseline; (iii) while precipitation projections are generally less reliable than temperature projections, model agreement in precipitation projections increases from RCP2.6 to RCP8.5, and from short-to long-term projections, indicating that long-term precipitation projections are generally more robust than their short-term counterparts and (iv) there is a consistent positive trend in frequency of extreme precipitation days (e.g. > 40 mm/day) for decades 2060s and beyond. These new climate projections should be used in future assessment of impact of climate change and adaptation planning. There is need to consider not just the mean climate projections, but also the more important extreme projections in impact studies and as well in adaptation planning.

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments obtained from statistical trials encodes a classical probability distribution. However, it is well known that an incompatible set of moments arises in the quantum scenario, when correlation outcomes associated with measurements on spatially separated entangled states are considered. This feature, viz., the incompatibility of moments with a joint probability distribution, is reflected in the violation of Bell inequalities. Here, we focus on sequential measurements on a single quantum system and investigate if moments and joint probabilities are compatible with each other. By considering sequential measurement of a dichotomic dynamical observable at three different time intervals, we explicitly demonstrate that the moments and the probabilities are inconsistent with each other. Experimental results using a nuclear magnetic resonance system are reported here to corroborate these theoretical observations, viz., the incompatibility of the three-time joint probabilities with those extracted from the moment sequence when sequential measurements on a single-qubit system are considered.

Plasmonic tuning of photoluminescence from semiconducting quantum dot assemblies

We report tuning of photoluminescence enhancement and quenching from closed packed monolayers of cadmium selenide quantum dots doped with gold nanoparticles. Plasmon-mediated control of the emission intensity from the monolayers is achieved by varying the size and packing density of the quantum dots as well as the doping concentration of gold nanoparticles. We observe a unique packing density dependent crossover from enhancement to quenching and vice versa for fixed size of quantum dots and doping concentration of gold nanoparticles. We suggest that this behavior is indicative of a crossover from single particle to collective emission from quantum dots mediated by gold nanoparticles.

Analysis of voltage stability in multi-infeed HVDC systems with STATCOM

This paper presents the modelling and analysis of voltage stability at AC commutation bus in LCC (Line commutated converters) based multi-infeed HVDC system. The paper also presents the analysis of effects of various operating control modes in HVDC as well as location of disturbance on the voltage stability of the system under study. A new method of modelling the LCC converters as time varying admittance at the AC commutation bus is also presented in this paper. In this paper, the modelling of STATCOM for provision of dynamic voltage support at one of the AC buses of the HVDC system is presented. The reactive power injected by STATCOM is controlled by regulating the voltage of the AC bus to which STATCOM is connected. The case study also discusses the effects of various possible combinations of location of STATCOM and disturbance considered, on the voltage stability of the multi-infeed HVDC system.

Quantum entropic ambiguities: Ethylene

In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are, in general, different. Therefore, one reaches the remarkable possibility that there may be many entropies for a given state R. Sorkin (private communication)]. This ambiguity in entropy can often be traced to a gauge symmetry emergent from the nontrivial topological character of the configuration space of the underlying system. It can also happen in finite-dimensional matrix models. In the present work, we discuss this entropy ambiguity and its consequences for an ethylene molecule. This is a very simple and well-known system, where these notions can be put to tests. Of particular interest in this discussion is the fact that the change of the density matrix with the corresponding entropy increase drives the system towards the maximally disordered state with maximum entropy, where Boltzman's formula applies. Besides its intrinsic conceptual interest, the simplicity of this model can serve as an introduction to a similar discussion of systems such as colored monopoles and the breaking of color symmetry.

Dielectric and electrical conductivity properties of multi-stage spark plasma sintered HA-CaTiO3 composites and comparison with conventionally sintered materials

One of the different issues limiting the wider application of monolithic hydroxyapatite (HA) as an ideal bone replacement material is the lack of reasonably good electrical transport properties. The comprehensive electrical property characterization to evaluate the efficacy of processing parameters in achieving the desired combination of electroactive properties is considered as an important aspect in the development of HA-based bioactive material. In this perspective, the present work reports the temperature (RT-200 degrees C) and frequency (100 Hz-1 MHz) dependent dielectric properties and AC conductivity for a range of HA-CaTiO3 (HA-CT) composites, densified using both conventional pressureless sintering in air as well as spark plasma sintering in vacuum. Importantly, the AC conductivity of spark plasma sintered ceramics similar to upto 10(-5) (Omega cm)(-1)] are found to be considerably higher than the corresponding pressureless sintered ceramics similar to upto 10(-8) (Omega cm)(-1)]. Overall, the results indicate the processing route dependent functional properties of HA-CaTiO3 composites as well as related advantages of spark plasma sintering route. (C) 2013 Elsevier Ltd. All rights reserved.