Arnol’d diffusion in a system with 2.5 degrees of freedom: Classical and quantum mechanical approaches

Arnol’d diffusion, a universal phenomenon in nonlinear dynamics, is analyzed for a model system with 2.5 degrees of freedom. Only the three primary order resonances are taken into account, and the results obtained by using classical and quantum mechanical approaches are compared. It is shown that the parameter dependence of the rate of quantum Arnol’d diffusion is similar to the classical one, but the quantum diffusion coefficient is smaller by approximately an order of magnitude. It is found that the existence of a threshold with respect to perturbation parameters, pointed out earlier, is not an indispensable feature of quantum Arnol’d diffusion. It is shown that a quantum system with weakly overlapping resonances can exhibit mixed dynamics that has no classical counterpart (diffusion along a resonance superimposed by oscillations across the overlapped resonances).     

管内两层介质入口段扩散混合的耦合换热研究

对圆管内辐射物性不同的两层介质层流入口段,采用SIMPLEC算法与蒙特卡罗法数值模拟了二维稳态流动与扩散混合时的辐射-对流耦合换热。通过计算,分析了介质层几何参数、介质物性与流动参数对组份分布与耦合换热的影响。结果表明,介质组分的扩散混合对耦合换热存在明显的影响区域,且该影响区大于组分的扩散混合区;外层介质的吸收系数、入口截面的相对厚度对耦合换热的影响基本一致;质扩散系数对耦合换热的影响很小,入口雷诺数的增加会抑制质扩散。     

The Ξ~* K and ?η Interaction Within a Chiral Unitary Approach

In this work we study the interaction of the coupled channels ?η and Ξ* ˉK within the chiral unitary approach.The systems under consideration have total isospins 0,strangeness S =-3,and spin 3/2.We study the s wave interaction which implies that the possible resonances generated in the system can have spin-parity JP= 3/2-.The unitary amplitudes in coupled channels develop poles that can be associated with some known baryonic resonances.We find there is a dynamically generated 3/2-? state with mass around 1800 Me V,which is in agreement with the predictions of the five-quark model.     

Improved Spin-Echo-Edited NMR Diffusion Measurements

The need for simple and robust schemes for the analysis of ligand-protein binding has resulted in the development of diffusion-based NMR techniques that can be used to assay binding in protein solutions containing a mixture of several ligands. As a means of gaining spectral selectivity in NMR diffusion measurements, a simple experiment, the gradient modified spin-echo (GOSE), has been developed to reject the resonances of coupled spins and detect only the singlets in the (1)H NMR spectrum. This is accomplished by first using a spin echo to null the resonances of the coupled spins. Following the spin echo, the singlet magnetization is flipped out of the transverse plane and a dephasing gradient is applied to reduce the spectral artifacts resulting from incomplete cancellation of the J-coupled resonances. The resulting modular sequence is combined here with the BPPSTE pulse sequence; however, it could be easily incorporated into any pulse sequence where additional spectral selectivity is desired. Results obtained with the GOSE-BPPSTE pulse sequence are compared with those obtained with the BPPSTE and CPMG-BPPSTE experiments for a mixture containing the ligands resorcinol and tryptophan in a solution of human serum albumin.     

A composite light scalar,electro-weak symmetry breaking and the recent LHC searches

We construct a model in which electro-weak symmetry breaking is induced by a strongly coupled sector, which is described in terms of a five-dimensional model in the spirit of the bottom-up approach to holography. We compute the precision electro-weak parameters, and identify regions of parameter space allowed by indirect tests. We compute the spectrum of scalar and vector resonances, which contains a set of parametrically light states that can be identified with the electro-weak gauge bosons and a light dilaton. There is then a little desert, up to 2–3 TeV, where towers of resonances of the vector, axial-vector and scalar particles appear.     

Spectroscopy of a driven solid-state qubit coupled to a structured environment

We study the asymptotic dynamics of a driven spin-boson system where the environment is formed by a broadened localized mode. Upon exploiting an exact mapping, an equivalent formulation of the problem in terms of a quantum two-state system (qubit) coupled to a harmonic oscillator which is itself Ohmically damped, is found. We calculate the asymptotic population difference of the two states in two complementary parameter regimes. For weak damping and low temperature, a perturbative Floquet-Born-Markovian master equation for the qubit-oscillator system can be solved. We find multi-photon resonances corresponding to transitions in the coupled quantum system and calculate their line-shape analytically. In the complementary parameter regime of strong damping and/or high temperatures, non-perturbative real-time path integral techniques yield analytic results for the resonance line shape. In both regimes, we find very good agreement with exact results obtained from a numerical real-time path-integral approach. Finally, we show for the case of strong detuning between qubit and oscillator that the width of the n-photon resonance scales with the nth Bessel function of the driving strength in the weak-damping regime.     

Multiple Spatial Coherence Resonances and Spatial Patterns in a Noise-Driven Heterogeneous Neuronal Network

Heterogeneity of the neurons and noise are inevitable in the real neuronal network. In this paper, Gaussian white noise induced spatial patterns including spiral waves and multiple spatial coherence resonances are studied in a network composed of Morris-Lecar neurons with heterogeneity characterized by parameter diversity. The relationship between the resonances and the transitions between ordered spiral waves and disordered spatial patterns are achieved. When parameter diversity is introduced, the maxima of multiple resonances increases first, and then decreases as diversity strength increases, which implies that the coherence degrees induced by noise are enhanced at an intermediate diversity strength. The synchronization degree of spatial patterns including ordered spiral waves and disordered patterns is identified to be a very low level. The results suggest that the nervous system can profit from both heterogeneity and noise, and the multiple spatial coherence resonances are achieved via the emergency of spiral waves instead of synchronization patterns.     

Analysis of a spray diffusion flame and its extinction in a shear layer

A new semi-analytical solution for a laminar spray diffusion flame in the shear layer between fuel and oxidant streams is developed. The Stokes number is identified as a small spray droplet-related parameter to be used in a perturbation analysis of the liquid phase governing equations. Appropriate specification of an additional parameter ensures that similarity is achieved so that the concentration field of the liquid in the spray can be readily found. The coupled gas-phase equations are treated using the usual inverse of the large Zeldovitch number for the asymptotic analysis. Numerical results demonstrate how the distribution of the liquid phase in the developing shear layer between two unidirectional gas streams flowing over one another with (the possibility of) dissimilar velocities in their respective free-streams influences the flame shape, location, fuel vapour and temperature fields. An extinction analysis enables a parametric mapping of conditions for extinguishment of the spray diffusion flames to be drawn.     

Feedback control in a coupled Brownian ratchet

On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally, the influences of the time delay, the coupling constant, and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated. The centre-of-mass velocity of two coupled Brownian particles, the average effective diffusion coefficient, and the Pe number are calculated. It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential. It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case. It is expected that the results obtained here may be observed in some physical and biological systems.     

Numerical studies of hyperbolic manifolds supporting diffusion in symplectic mappings

Diffusion in generic quasi integrable systems at small values of the perturbing parameters has been a very studied subject since the pioneering work of Arnold [3]. For moderate values of the perturbing parameter a different kind of diffusion occurs, the so called Chirikov diffusion, since the Chirikov’s papers [11, 13]. The two underlying mechanisms are different, the first has an analytic demonstration only on specific models, the second is based on an heuristic argument. Even if the relation between chaos and diffusion is far to be completely understood, a key role is played by the topology of hyperbolic manifolds related to the resonances. Different methods can be found in the literature for the detection of hyperbolic manifolds, at least for two dimensional systems. For higher dimensional ones some sophisticated methods have been recently developed (for a review see [55]). In this paper we review some of these methods and an easy tool of detection of invariant manifolds that we have developed based on the Fast Lyapunov Indicator. The relation between the topology of hyperbolic manifolds and diffusion is discussed in the framework of Arnold diffusion.     

Feshbach resonances in the 6Li-40K Fermi-Fermi mixture: elastic versus inelastic interactions

We present a detailed theoretical and experimental study of Feshbach resonances in the ⁶Li-⁴⁰K mixture. Particular attention is given to the inelastic scattering properties, which have not been considered before. As an important example, we thoroughly investigate both elastic and inelastic scattering properties of a resonance that occurs near 155?G. Our theoretical predictions based on a coupled channels calculation are found in excellent agreement with the experimental results. We also present theoretical results on the molecular state that underlies the 155?G resonance, in particular concerning its lifetime against spontaneous dissociation. We then present a survey of resonances in the system, fully characterizing the corresponding elastic and inelastic scattering properties. This provides the essential information to identify optimum resonances for applications relying on interaction control in this Fermi-Fermi mixture.     

Entanglement generation through the interplay of harmonic driving and interaction in coupled superconducting qubits

We study the manipulation of quantum entanglement by periodic external fields. As an entanglement measure we compute numerically the concurrence of two coupled superconducting qubits both driven by a dc + ac external control parameter. We show that when the driving term of the Hamiltonian commutes with the qubit–qubit interaction term, it is possible to create or destroy entanglement in a controlled way by tuning the system at or near multiphoton resonances. On the other hand, when the driving does not commute with the qubit–qubit interaction, the control and generation of entanglement induced by the driving field is more robust and extended in parameter space, beyond the multiphoton resonances.     

Exploring an ultracold fermi-fermi mixture: interspecies feshbach resonances and scattering properties of 6Li and 40K

We report on the observation of Feshbach resonances in an ultracold mixture of two fermionic species, (6)Li and (40)K. The experimental data are interpreted using a simple asymptotic bound state model and full coupled channels calculations. This unambiguously assigns the observed resonances in terms of various s- and p-wave molecular states and fully characterizes the ground-state scattering properties in any combination of spin states.     

Detection of homonuclear decoupled in vivo proton NMR spectra using constant time chemical shift encoding: CT-PRESS

A new pulse sequence, termed CT-PRESS, is presented, which allows the detection of in vivo ¹H NMR spectra with effective homonuclear decoupling. A PRESS sequence with a short echo-time TE, used for spatial localization, is supplemented by an additional 180° pulse. The temporal position of this 180° pulse is shifted within a series of experiments, while the time interval between signal excitation and detection is kept constant. CT-PRESS is a two-dimensional (2D) spectroscopic experiment as far as data acquisition and processing are concerned, although only diagonal signals are generated in the 2D spectrum. However, since the principle of constant time chemical shift encoding is used in the t₁ domain, effective homonuclear decoupling is obtained by projecting the 2D spectrum onto the corresponding f₁ axis. Thus, good spectral resolution and high signal-to-noise ratio are obtained. The main advantage, as compared to localized 2D J-resolved MRS, is that optimized experiments can be performed for coupled resonances of interest by choosing the sequence parameters dependent on the type of multiplets, the J-coupling constants and T₂. Major fields of application will be parametric studies on coupled resonances, (e.g., T₁, diffusion behavior or magnetization transfer) and/or the detection of spatial and temporal changes of metabolites with coupled spin systes.     

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

We use a non-perturbative approach which combines coupled channel Lippmann-Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f₀ and a₀ resonances. The ππ → ππ, phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the π⁰η and mass distributions in the T = 1 channel. Furthermore, the total and partial strong decay widths of the f₀ and a₀ resonances are properly reproduced. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below GeV.     

\bar{K} Condensation in Neutron Star Matter with Δ Quartet

In the framework of relativistic mean field theory, the condensations of K^- and \bar{K}⁰ in neutron star matter including baryon octet and Δ quartet are studied. We find that in this case K^- and \bar{K}⁰ condensations canoccur at relative shallow optical potential depth of \bar{K} from -80 MeV to -160 MeV. Both K^- and \bar{K}⁰ condensations favor the appearances of Δ resonances. With \bar{K} condensations all the Δ quartet can appear well inside the maximum mass stars. The appearances of Δ resonances change the composition and distribution of particles at high densities. The populations ofΔ resonances can enhance K^- condensation. It is found that in the core of massive neutron stars, neutron star matter includes rich particle species, such as antikaons, baryon octet, and Δ quartet. In the presence of Δ resonances and \bar{K} condensation, the EOS becomes softer and results in smaller maximum mass stars. Furthermore the impact of antikaon condensations,hyperons, and Δ resonances on direct Urca process with nucleons is also discussed briefly.     

Spiral Waves and Multiple Spatial Coherence Resonances Induced by Colored Noise in Neuronal Network

Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bifurcation on invariant circle,coupled to its nearest neighbors by electronic coupling.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity.By calculating spatial structure function and signal-to-noise ratio(SNR),it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered,respectively.SNR manifest multiple local maximal peaks,indicating that the colored noise can induce multiple spatial coherence resonances.The maximal SNR values decrease as the correlation time of the noise increases.These results not only provide an example of multiple resonances,but also show that Gaussian colored noise play constructive roles in neuronal network.     

Diffusion,effusion, and chaotic scattering: An exactly solvable Liouvillian dynamics

We study diffusion and chaotic scattering in a chain of baker maps coupled together which forms an area-preserving mapping of an infinitely extended strip onto itself. This exactly solvable mapping sustains chaotic behaviors and diffusion processes. The relationship between the diffusion coefficient, the Lyapunov exponent, and the entropy per unit time is derived. The long-lived classical resonances of the Liouville evolution operator are proved to converge toward the eigenvalues of the phenomenological diffusion equation. In this sense, there is a quasi-isomorphism between the resonance spectrum of the Liouville evolution and the eigenvalue spectrum of the phenomenological diffusion equation. Furthermore, we show that a fractal repeller is associated to each non-equilibrium state in the isolated and finite multibaker chain. The nonequilibrium states are all unstable with respect to the equilibrium, validating a weak form of the second principle of thermodynamics for the present dynamical system. Consequences of nonequilibrium fractals on classical measurements are discussed. We then describe the open multibaker chain as a scattering system. Fractal properties of chaotic scattering are here shown to be related to diffusion in the chain.     

Quantum diffusion of H/Ni(111) through a Monte Carlo wave function formalism

We consider a quantum system coupled to a dissipative background with many degrees of freedom using the Monte Carlo wave function method. Instead of dealing with a density matrix which can be very highly dimensional, the method consists of integrating a stochastic Schr?dinger equation with a non-Hermitian damping term in the evolution operator, and with random quantum jumps. The method is applied to the diffusion of hydrogen on the Ni(111) surface below 100 K. We show that the recent experimental diffusion data for this system can be understood through an interband activation process, followed by quantum tunneling.     

Phase space structure and chaotic scattering in near-integrable systems

We investigate the bifurcation phenomena and the change in phase space structure connected with the transition from regular to chaotic scattering in classical systems with unbounded dynamics. The regular systems discussed in this paper are integrable ones in the sense of Liouville, possessing a degenerated unstable periodic orbit at infinity. By means of a McGehee transformation the degeneracy can be removed and the usual Melnikov method is applied to predict homoclinic crossings of stable and unstable manifolds for the perturbed system. The chosen examples are the perturbed radial Kepler problem and two kinetically coupled Morse oscillators with different potential parameters which model the stretching dynamics in ABC molecules. The calculated subharmonic and homoclinic Melnikov functions can be used to prove the existence of chaotic scattering and of elliptic and hyperbolic periodic orbits, to calculate the width of the main stochastic layer and of the resonances, and to predict the range of initial conditions where singularities in the scattering function are found. In the second example the value of the perturbation parameter at which channel transitions set in is calculated. The theoretical results are supplemented by numerical experiments.