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.

Physics-Based Band Gap Model for Relaxed and Strained 100] Silicon Nanowires

In this paper, we propose a physics-based simplified analytical model of the energy band gap and electron effective mass in a relaxed and strained rectangular 100] silicon nanowires (SiNWs). Our proposed formulation is based on the effective mass approximation for the nondegenerate two-band model and 4 x 4 Luttinger Hamiltonian for energy dispersion relation of conduction band electrons and the valence band heavy and light holes, respectively. Using this, we demonstrate the effect of the uniaxial strain applied along 100]-direction and a biaxial strain, which is assumed to be decomposed from a hydrostatic deformation along 001] followed by a uniaxial one along the 100]-direction, respectively, on both the band gap and the transport and subband electron effective masses in SiNW. Our analytical model is in good agreement with the extracted data using the extended-Huckel-method-based numerical simulations over a wide range of device dimensions and applied strain.

Carbon dioxide detection by boron nitride nanotubes

The effect of gas molecule adsorption is investigated on the density of states of (9,0) zigzag boron nitride nanotube within a random tight-binding Hamiltonian model. The Green function approach and coherent potential approximation have been implemented. The results show that the adsorption of carbon dioxide gas molecules by boron atoms only leads to a donor type semiconductor while the adsorption by nitrogen atoms only leads to an acceptor. Since the gas molecules are adsorbed by both boron and nitrogen atoms, a reduction of the band gap is found. In all cases, increasing the gas concentration causes an increase in the height of the peaks in the band gap. This is due to an increasing charge carrier concentration induced by adsorbed gas molecules.

ENTANGLEMENT IN A 3-SPIN HEISENBERG-XY CHAIN WITH NEAREST-NEIGHBOR INTERACTIONS, SIMULATED IN AN NMR QUANTUM SIMULATOR

The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. Phys. Rev. A 72 (2005) 012331]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits, respectively after the unitary evolution of the XY Hamiltonian.

Automatic energy-momentum conserving time integrators for hyperelastic waves

An energy-momentum conserving time integrator coupled with an automatic finite element algorithm is developed to study longitudinal wave propagation in hyperelastic layers. The Murnaghan strain energy function is used to model material nonlinearity and full geometric nonlinearity is considered. An automatic assembly algorithm using algorithmic differentiation is developed within a discrete Hamiltonian framework to directly formulate the finite element matrices without recourse to an explicit derivation of their algebraic form or the governing equations. The algorithm is illustrated with applications to longitudinal wave propagation in a thin hyperelastic layer modeled with a two-mode kinematic model. Solution obtained using a standard nonlinear finite element model with Newmark time stepping is provided for comparison. (C) 2012 Elsevier B.V. All rights reserved.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits

Levy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases. DOI: 10.1103/PhysRevE.86.061105

Fidelity susceptibility of one-dimensional models with twisted boundary conditions

Recently it has been shown that the fidelity of the ground state of a quantum many-body system can be used todetect its quantum critical points (QCPs). If g denotes the parameter in the Hamiltonian with respect to which the fidelity is computed, we find that for one-dimensional models with large but finite size, the fidelity susceptibility chi(F) can detect a QCP provided that the correlation length exponent satisfies nu < 2. We then show that chi(F) can be used to locate a QCP even if nu >= 2 if we introduce boundary conditions labeled by a twist angle N theta, where N is the system size. If the QCP lies at g = 0, we find that if N is kept constant, chi(F) has a scaling form given by chi(F) similar to theta(-2/nu) f (g/theta(1/nu)) if theta << 2 pi/N. We illustrate this both in a tight-binding model of fermions with a spatially varying chemical potential with amplitude h and period 2q in which nu = q, and in a XY spin-1/2 chain in which nu = 2. Finally we show that when q is very large, the model has two additional QCPs at h = +/- 2 which cannot be detected by studying the energy spectrum but are clearly detected by chi(F). The peak value and width of chi(F) seem to scale as nontrivial powers of q at these QCPs. We argue that these QCPs mark a transition between extended and localized states at the Fermi energy. DOI: 10.1103/PhysRevB.86.245424

RRI-GBT MULTI-BAND RECEIVER: MOTIVATION, DESIGN, AND DEVELOPMENT

We report the design and development of a self-contained multi-band receiver (MBR) system, intended for use with a single large aperture to facilitate sensitive and high time-resolution observations simultaneously in 10 discrete frequency bands sampling a wide spectral span (100-1500 MHz) in a nearly log-periodic fashion. The development of this system was primarily motivated by need for tomographic studies of pulsar polar emission regions. Although the system design is optimized for the primary goal, it is also suited for several other interesting astronomical investigations. The system consists of a dual-polarization multi-band feed (with discrete responses corresponding to the 10 bands pre-selected as relatively radio frequency interference free), a common wide-band radio frequency front-end, and independent back-end receiver chains for the 10 individual sub-bands. The raw voltage time sequences corresponding to 16 MHz bandwidth each for the two linear polarization channels and the 10 bands are recorded at the Nyquist rate simultaneously. We present the preliminary results from the tests and pulsar observations carried out with the Robert C. Byrd Green Bank Telescope using this receiver. The system performance implied by these results and possible improvements are also briefly discussed.

Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy. DOI: 10.1103/PhysRevA.87.013628

k.p based closed form energy band gap and transport electron effective mass model for 100] and 110] relaxed and strained Silicon nanowire

In this paper, we address a physics based closed form model for the energy band gap (E-g) and the transport electron effective mass in relaxed and strained 100] and 110] oriented rectangular Silicon Nanowire (SiNW). Our proposed analytical model along 100] and 110] directions are based on the k.p formalism of the conduction band energy dispersion relation through an appropriate rotation of the Hamiltonian of the electrons in the bulk crystal along 001] direction followed by the inclusion of a 4 x 4 Luttinger Hamiltonian for the description of the valance band structure. Using this, we demonstrate the variation in Eg and the transport electron effective mass as function of the cross-sectional dimensions in a relaxed 100] and 110] oriented SiNW. The behaviour of these two parameters in 100] oriented SiNW has further been studied with the inclusion of a uniaxial strain along the transport direction and a biaxial strain, which is assumed to be decomposed from a hydrostatic deformation along 001] with the former one. In addition, the energy band gap and the effective mass of a strained 110] oriented SiNW has also been formulated. Using this, we compare our analytical model with that of the extracted data using the nearest neighbour empirical tight binding sp(3)d(5)s* method based simulations and has been found to agree well over a wide range of device dimensions and applied strain. (C) 2012 Elsevier Ltd. All rights reserved.

The dynamics between forward citations and price of singleton patents

In recent years, business practitioners are seen valuing patents on the basis of the market price that the patent can attract. Researchers have also looked into various patent latent variables and firm variables that influence the price of a patent. Forward citations of a patent are shown to play a role in determining price. Using patent auction price data (of Ocean Tomo now ICAP patent brokerage), we delve deeper into of the role of forward citations. The successfully sold 167 singleton patents form the sample of our study. We found that, it is mainly the right tail of the citation distribution that explains the high prices of the patents falling on the right tail of the price distribution. There is consistency in the literature on the positive correlation between patent prices and forward citations. In this paper, we go deeper to understand this linear relationship through case studies. Case studies of patents with high and low citations are described in this paper to understand why some patents attracted high prices. We look into the role of additional patent latent variables like age, technology discipline, class and breadth of the patent in influencing citations that a patent receives.

Comparison of North American universities with and without medical schools and their technology transfer initiatives

Empirical research available on technology transfer initiatives is either North American or European. Literature over the last two decades shows various research objectives such as identifying the variables to be measured and statistical methods to be used in the context of studying university based technology transfer initiatives. AUTM survey data from years 1996 to 2008 provides insightful patterns about the North American technology transfer initiatives, we use this data in our paper. This paper has three sections namely, a comparison of North American Universities with (n=1129) and without Medical Schools (n=786), an analysis of the top 75th percentile of these samples and a DEA analysis of these samples. We use 20 variables. Researchers have attempted to classify university based technology transfer initiative variables into multi-stages, namely, disclosures, patents and license agreements. Using the same approach, however with minor variations, three stages are defined in this paper. The first stage is to do with inputs from R&D expenditure and outputs namely, invention disclosures. The second stage is to do with invention disclosures being the input and patents issued being the output. The third stage is to do with patents issued as an input and technology transfers as outcomes.

Fermions in synthetic non-Abelian gauge potentials: rashbon condensates to novel Hamiltonians

Recent advances in the generation of synthetic gauge fields in cold atomic systems have stimulated interest in the physics of interacting bosons and fermions in them. In this paper, we discuss interacting two-component fermionic systems in uniform non-Abelian gauge fields that produce a spin-orbit interaction and uniform spin potentials. Two classes of gauge fields discussed include those that produce a Rashba spin-orbit interaction and the type of gauge fields (SM gauge fields) obtained in experiments by the Shanxi and MIT groups. For high symmetry Rashba gauge fields, a two-particle bound state exists even for a vanishingly small attractive interaction described by a scattering length. Upon increasing the strength of a Rashba gauge field, a finite density of weakly interacting fermions undergoes a crossover from a BCS like ground state to a BEC state of a new kind of boson called the rashbon whose properties are determined solely by the gauge field and not by the interaction between the fermions. The rashbon Bose-Einstein condensate (RBEC) is a quite intriguing state with the rashbon-rashbon interactions being independent of the fermion-fermion interactions (scattering length). Furthermore, we show that the RBEC has a transition temperature of the order of the Fermi temperature, suggesting routes to enhance the transition temperatures of weakly interacting superfluids by tuning the spin-orbit coupling. For the SM gauge fields, we show that in a regime of parameters, a pair of particles with finite centre-of-mass momentum is the most strongly bound. In other regimes of centre-of-mass momenta, there is no two-body bound state, but a resonance like feature appears in the scattering continuum. In the many-body setting, this results in flow enhanced pairing. Also, strongly interacting normal states utilizing the scattering resonance can be created opening the possibility of studying properties of helical Fermi liquids. This paper contains a general discussion of the physics of Feshbach resonance in a non-Abelian gauge field, where several novel features such as centre-of-mass-momentum-dependent effective interactions are shown. It is also shown that a uniform non-Abelian gauge field in conjunction with a spatial potential can be used to generate novel Hamiltonians; we discuss an explicit example of the generation of a monopole Hamiltonian.

Adiabatic eigenfunction-based approach for coherent excitation transfer: An almost analytical treatment of the Fenna-Matthews-Olson complex

We suggest a method of studying coherence in finite-level systems coupled to the environment and use it for the Hamiltonian that has been used to describe the light-harvesting pigment-protein complex. The method works with the adiabatic states and transforms the Hamiltonian to a form in which the terms responsible for decoherence and population relaxation are separated out. Decoherence is then accounted for nonperturbatively and population relaxation using a Markovian master equation. Almost analytical results can be obtained for the seven-level system, and the calculations are very simple for systems with more levels. We apply the treatment to the seven-level system, and the results are in excellent agreement with the exact numerical results of Nalbach et al. Nalbach, Braun, and Thorwart, Phys. Rev. E 84, 041926 (2011)]. Our approach is able to account for decoherence and population relaxation separately. It is found that decoherence causes only damping of oscillations and does not lead to transfer to the reaction center. Population relaxation is necessary for efficient transfer to the reaction center, in agreement with earlier findings. Our results show that the transformation to the adiabatic basis followed by a Redfield type of approach leads to results in good agreement with exact simulation.