On the quantum mechanical propagator for driven coupled harmonic oscillators

The exact propagator beyond and at caustics for a pair of coupled and driven oscillators with different frequencies and masses is calculated using the path-integral approach. The exact wavefunctions and energies are also presented. Finally the propagator is re-calculated through an alternative method, using the δfunction. © 1992 IOP Publishing Ltd.

Fourier´s law from a chain of coupled anharmonic oscillators under energy conserving shot noise.

We analyze the transport of heat along a chain of particles interacting through anharmonic potentials consisting of quartic terms in addition to harmonic quadratic terms and subject to heat reservoirs at its ends. Each particle is also subject to an impulsive shot noise with exponentially distributed waiting times whose effect is to change the sign of its velocity, thus conserving the energy of the chain. We show that the introduction of this energy conserving stochastic noise leads to Fourier's law. That is for large system size L the heat current J behaves as J ‘approximately’ 1/L, which amounts to say that the conductivity k is constant. The conductivity is related to the current by J = kΔT/L, where ΔT is the difference in the temperatures of the reservoirs. The behavior of heat conductivity k for small intensities¸ of the shot noise and large system sizes L are obtained by assuming a scaling behavior of the type k = ‘L POT a Psi’(L’lambda POT a/b’) where a and b are scaling exponents. For the pure harmonic case a = b = 1, characterizing a ballistic conduction of heat when the shot noise is absent. For the anharmonic case we found values for the exponents a and b smaller then 1 and thus consistent with a superdiffusive conduction of heat without the shot noise. We also show that the heat conductivity is not constant but is an increasing function of temperature.

Bright entanglement and the Einstein-Podolsky-Rosen paradox with coupled parametric oscillators

We show that two evanescently coupled chi((2)) parametric oscillators provide a tunable bright source of quadrature squeezed light, Einstein-Podolsky-Rosen correlations and quantum entanglement. Analysing the system in the above threshold regime, we demonstrate that these properties can be controlled by adjusting the coupling strengths and the cavity detunings. As this can be implemented with integrated optics, it provides a possible route to rugged and stable EPR sources. (C) 2005 Elsevier B.V. All rights reserved.

Collective behaviour in a square lattice of driven Duffing resonators coupled to van der Pol oscillators

The global and local synchronisation of a square lattice composed of alternating Duffing resonators and van der Pol oscillators coupled through displacement is studied. The lattice acts as a sensing device in which the input signal is characterised by an external driving force that is injected into the system through a subset of the Duffing resonators. The parameters of the system are taken from MEMS devices. The effects of the system parameters, the lattice architecture and size are discussed.

Study of synchronisation in chains of coupled non-linear oscillators and resonators

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Emergent behaviour in arrays of coupled nonlinear oscillators

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Geometric quantum computation using fictitious spin-1/2 subspaces of strongly dipolar coupled nuclear spins

Geometric phases have been used in NMR to implement controlled phase shift gates for quantum-information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems by using nonadiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete 2 pi rotation. A detailed theoretical explanation of nonadiabatic geometric phases in NMR is given by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm, and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.

Dipolar cross-correlation effects in the nuclear overhauser experiments of weakly and strongly coupled spins

The effect of dipolar cross correlation in 1H---1H nuclear Overhauser effect experiments is investigated by detailed calculation in an ABX spin system. It is found that in weakly coupled spin systems, the cross-correlation effects are limited to single-quantum transition probabilities and decrease in magnitude as ωτc increases. Strong coupling, however, mixes the states and the cross correlations affect the zero-quantum and double-quantum transition probabilities as well. The effect of cross correlation in steady-state and transient NOE experiments is studied as a function of strong coupling and ωτc. The results for steady-state NOE experiments are calculated analytically and those for transient NOE experiments are calculated numerically. The NOE values for the A and B spins have been calculated by assuming nonselective perturbation of all the transitions of the X spin. A significant effect of cross correlation is found in transient NOE experiments of weakly as well as strongly coupled spins when the multiplets are resolved. Cross correlation manifests itself largely as a multiplet effect in the transient NOE of weakly coupled spins for nonselective perturbation of all X transitions. This effect disappears for a measuring pulse of 90° or when the multiplets are not resolved. For steady-state experiments, the effect of cross correlation is analytically zero for weakly coupled spins and small for strongly coupled spins.

Triple resonance, triple-quantum NMR studies of dipolar coupled spin systems

Multiple quantum-single quantum correlation experiments are employed for spectral simplification and determination of the relative signs of the couplings. In this study, we have demonstrated the excitation of three nuclei, triple quantum coherences and discussed the information obtainable from such experiments. The experiments have been carried out on doubly labeled acetonitrile and fluoroacetonitrile aligned in liquid crystalline media. The experiment is advantageous in providing many spectral parameters from a single experiment. The coherence pathways involved in the pulse sequence are described using product operators. (C) 2011 Elsevier Inc. All rights reserved.

Development of novel multiple quantummethodologies for the analyses of complex protonNMR spectra of scalar coupled spins

One of the significant advancements in Nuclear Magnetic Resonance spectroscopy (NMR) in combating the problem of spectral complexity for deriving the structure and conformational information is the incorporation of additional dimension and to spread the information content in a two dimensional space. This approach together with the manipulation of the dynamics of nuclear spins permitted the designing of appropriate pulse sequences leading to the evolution of diverse multidimensional NMR experiments. The desired spectral information can now be extracted in a simplified and an orchestrated manner. The indirect detection of multiple quantum (MQ) NMR frequencies is a step in this direction. The MQ technique has been extensively used in the study of molecules aligned in liquid crystalline media to reduce spectral complexity and to determine molecular geometries. Unlike in dipolar coupled systems, the size of the network of scalar coupled spins is not big in isotropic solutions and the MQ 1H detection is not routinely employed,although there are specific examples of spin topology filtering. In this brief review, we discuss our recent studies on the development and application of multiple quantum correlation and resolved techniques for the analyses of proton NMR spectra of scalar coupled spins.

Biodiesel Exhaust Treatment with Dielectric Barrier Discharges Coupled with Industrial Waste Byproducts

Biodiesel run engines are gaining popularity since the last few years as a viable alternative to conventional petro-diesel based engines. In biodiesel exhaust the content of volatile organic compounds, oil mist, and mass of particulate matter is considerably lower. However, the concentration of oxides of nitrogen (NOx) is relatively higher. In this paper the biodiesel exhaust from a stationary engine is treated under controlled laboratory conditions for removal of NOx using dielectric barrier discharge plasma in cascade with adsorbents prepared from abundantly available industrial waste byproducts like red mud and copper slag. Results were compared with gamma-alumina, a commercial adsorbent. Two different dielectric barrier discharge (DBD) reactors were tested for their effectiveness under Repetitive pulses /AC energization. NOx removal as high as 80% was achieved with pulse energized reactors when cascaded with red mud as adsorbent.

Nonlinear Fluid Damping In Structure-Wake Oscillators In Modeling Vortex-Induced Vibrations

A Nonlinear Fluid Damping (NFD) in the form of the square-velocity is applied in the response analysis of Vortex-induced Vibrations (VIV). Its nonlinear hydrodynamic effects oil the coupled wake and structure oscillators are investigated. A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics, such as the amplification of body displacement at lock-in and frequency lock-ill, both at high and low mass ratios. Particularly, the predicted peak amplitude of the body in the Griffin plot is ill good agreement with experimental data and empirical equation, indicating the significant effect of the NFD on the structure motion.

Dynamics of femtosecond laser pulse induced damage in multilayers

We report the single-shot damage thresholds of MgF2/ZnS onmidirectional reflector for laser pulse durations from 50 A to 900 fs. A coupled dynamic model is applied to study the damage mechanisms, in which we consider not only the electronic excitation of the material, but also the influence of this excitation-induced changes in the complex refractive index of material on the laser pulse itself. The results indicate that this feedback effect plays a very important role during the damage of material. Based on this model, we calculate the threshold fluences and the time-resolved excitation process of the multiplayer. The theoretical calculations agree well with our experimental results. (c) 2005 Elsevier B.V. All rights reserved.

Pulse shaping properties of volume holographic gratings in anisotropic media

Based on a modified coupled wave theory, the pulse shaping properties of volume holographic gratings (VHGs) in anisotropic media VHGs are studied systematically. Taking photorefractive LiNbO3 crystals as an example, the combined effect that the grating parameters, the dispersion and optical anisotropy of the crystal, the pulse width, and the polarization state of the input ultrashort pulsed beam (UPB) have on the pulse shaping properties are considered when the input UPB with arbitrary polarization state propagates through the VHG. Under the combined effect, the diffraction bandwidth, pulse profiles of the diffracted and transmitted pulsed beams, and the total diffraction efficiency are shown. The studies indicate that the properties of the shaping of the o and e components of the input UPB in the crystal are greatly different; this difference can be used for pulse shaping applications. (c) 2006 Optical Society of America.

XPM-induced pulse compression in birefringent dispersion decreasing fiber

The pulse compression induced by cross-phase modulation in birefringent dispersion decreasing fiber is discussed theoretically by solving the coupled Schrodinger equations which include the contribution of the high-order non-linear effects, and third-order dispersion. In particular, it is found that a high quality compressed signal pulse can be obtained by a pump pulse of low intense through the technique. The dependence of optimum compression on the non-linear factor N, time delay tau(d) and the dispersive ratio f is also discussed in detail. (c) 2005 Elsevier B.V. All rights reserved.