Resonance phenomena in discrete systems with bichromatic input signal

We undertake a detailed numerical study of the twin phenomenon of stochastic and vibrational resonance in a discrete model system in the presence of bichromatic input signal. A two parameter cubic map is used as the model that combines the features of both bistable and threshold systems. In addition to the results already shown for continuous systems, our analysis brings out several interesting features both for vibrational and stochastic resonance, including the existence of a cross over behavior between the two. In the regime of vibrational resonance, it is shown that the additional high frequency forcing can change the effective value of the system parameter resulting in the shift of the bistable window. In the case of stochastic resonance, the study reveals a fundamental difference between the bistable and threshold mechanisms in the response, with respect to multisignal input.     

Analytical calculation of eigen-energies for lens-shaped quantum dot with finite barriers

With the help of metadynamics it is possible to calculate efficiently the free energy of systems displaying high energy barriers as a function of few selected “collective variables”. In doing this, the contribution of all the other degrees of freedom (“microscopic” variables) is averaged out and, thus, lost. In the following it is shown that it is possible to calculate the thermal average of these microscopic degrees of freedom during the metadynamics, not loosing this piece of information. The method is tested on a two-dimensional toy system and on a small molecule, that is dialanine.     

Chaotic dynamics of a parametrically modulated Josephson junction with quadratic damping

We study the chaotic dynamics of a parametrically modulated Josephson junction with quadratic damping. The Melnikov chaotic criteria are presented. When the perturbation conditions cannot be satisfied, numerical simulations demonstrate that the system can step into chaos via a quasi-periodic route with the increasing of the dc component of the modulation. However, it is numerically demonstrated that adding a feedback to the system can effectively suppress the chaos.     

Resonant effects in ballistic Josephson junctions

We study the Josephson effect in ballistic double-barrier SINIS planar junctions, consisting of bulk superconductors (S), a clean normal metal or semiconductor (N), and insulating interfaces (I) modeled as a δ-function potential-energy barriers. We solve the scattering problem based on the Bogoliubov-de Gennes equations and derive a general expression for the dc Josephson current, valid for arbitrary interfacial transparency, the Fermi wave vectors mismatch, and for different effective band masses. The effect of transmission resonances on the Josephson current and on the normal conductance is analyzed for short junctions. Curvature of the temperature dependence of the critical Josephson current is related to the presence of resonances at the Fermi level and to the interfacial transparency. For thin semiconductor layers with negative effective masses of the carriers, finite interfacial transparency and large Fermi wave vectors mismatch we find that an unusual and significant enhancement of both the normal conductance and the critical Josephson current occurs at low temperatures due to the presence of an evanescent mode localized at interfaces.     

Control coherence resonance by noise recycling

We study the effect of recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay, in a parameter region below the threshold of supercritical Hopf bifurcation, by focussing on the performance of noise induced oscillations and coherence resonance. For fixed noise intensity, the amplitude and signal-to-noise ratio of the oscillation show periodic dependences on the delay time. The optimal noise intensity for the occurrence of coherence resonance also shows a periodic dependence on the delay. A theoretical analysis based on the stochastic normal form theory is presented, which qualitatively reproduces the simulation results with good agreement. This work presents a possible strategy for controlling noise induced oscillations and coherence resonance by deliberately adjusting the parameters of the recycled noise.     

Quasiperiodically driven Josephson junctions: strange nonchaotic attractors, symmetries and transport

We consider the dynamics of the overdamped Josephson junction under the influence of an external quasiperiodic driving field. In dependence on parameter values either a quasiperiodic motion or a strange nochaotic attractor (SNA) can be observed. The latter corresponds to a resistive state in the current-voltage characteristics while for quasiperiodic motion a finite superconducting current exists for zero voltage. It is shown that in the case of SNA a nonzero mean voltage across the junction can appear due to symmetry breakings. Based on this observation a detailed symmetry consideration of the generalized equation of motion is performed and symmetry conditions ensuring zero mean voltage across the junction are found. Received 16 August 2001 and Received in final form 22 January 2002     

Finite size correction for fixed word length Zipf analysis

Zipf’s original law deals with the statistics of ranked words in natural languages. It has recently been generalized to “words” defined as n-tuples of symbols derived by translation of real-valued univariate timeseries into a literal sequence. We verify that the rank-frequency plot of these words shows, for fractional Brownian motion, the previously found power laws, but with large finite length corrections. We verify a finite size scaling ansatz for these corrections and, as aresult, demonstrate greatly improved estimates of the (generalized) Zipf exponents. This allows us to find the correct relation between the Zipf exponent and the Hurst exponent characterizing the fractional Brownian motion.     

Empirical analysis on a keyword-based semantic system

Keywords in scientific articles have found their significance in information filtering and classification. In this article, we empirically investigated statistical characteristics and evolutionary properties of keywords in a very famous journal, namely Proceedings of the National Academy of Science of the United States of America (PNAS), including frequency distribution, temporal scaling behavior, and decay factor. The empirical results indicate that the keyword frequency in PNAS approximately follows a Zipf’s law with exponent 0.86. In addition, there is a power-low correlation between the cumulative number of distinct keywords and the cumulative number of keyword occurrences. Extensive empirical analysis on some other journals’ data is also presented, with decaying trends of most popular keywords being monitored. Interestingly, top journals from various subjects share very similar decaying tendency, while the journals of low impact factors exhibit completely different behavior. Those empirical characters may shed some light on the in-depth understanding of semantic evolutionary behaviors. In addition, the analysis of keyword-based system is helpful for the design of corresponding recommender systems.     

Total entropy production fluctuation theorems in a nonequilibrium time-periodic steady state

We investigate the total entropy production of a Brownian particle in a driven bistable system. This system exhibits the phenomenon of stochastic resonance. We show that in the time-periodic steady state, the probability density function for the total entropy production satisfies Seifert’s integral and detailed fluctuation theorems over finite time trajectories.     

The influence of state dependent short range correlations on the depletion of the nuclear Fermi sea

The inlfuence of state dependent short range correlations on the occupation numbers of the single particle shell model orbits of the doubly closed shell nuclei¹⁶O and⁴⁰Ca is examined. The study shows that the effect of the state dependence of the short range correlations is rather small. The total depletion of the nuclear Fermi sea changes slightly compared with the one calculated by considering state independent short range correlations.     

Quantum cloning machine of a state in a belt of Bloch sphere

We analyze the problem of approximate quantum cloning when the quantum state is between two latitudes on the Bloch’s sphere. We present an analytical formula for the optimized 1-to-2 cloning. The formula unifies the universal quantum cloning (UQCM) and the phase covariant quantum cloning.     

Loop statistics in complex networks

We study a scaling property of the number M_h(N) of loops of size h in complex networks with respect to a network size N. For networks with a bounded second moment of degree, we find two distinct scaling behaviors: M_h(N) ~ (constant) and M_h(N) ~ lnN as N increases. Uncorrelated random networks specified only with a degree distribution and Markovian networks specified only with a nearest neighbor degree-degree correlation display the former scaling behavior, while growing network models display the latter. The difference is attributed to structural correlation that cannot be captured by a short-range degree-degree correlation.     

Quenching of the spin-dependent scattering of weakly interacting massive particles on heavy nuclei

We present calculations of the quenching of the spin-dependent elastic scattering cross section for dark matter WIMPs on heavy nuclei. The theory of finite Fermi systems was used to describe the behavior of the nuclear spin matrix elements in the nuclear medium. The results of the calculations for planned dark matter detector nuclei are not only always smaller than corresponding single particle estimations but in some cases also differ from the ones obtained by using measured nuclear magnetic moments.One of the authors (M.A.N.) wants to thank the Max-Planck-Institut für Kernphysik (Heidelberg, Germany) for the hospitality during the time in which this work was carried out, and the Deutscher Akademischer Austauschdienst (DAAD) for financial support.     

Load-dependent random walks on complex networks

Load-dependent random walks are used to investigate the evolution of load distribution in transportation network systems. The walkers hop to a node according to node load of the last time step. The preference of walks leads to a change in the load distribution. It changes from degree-dependent distribution in the case of non-preference walks to eigenvector-centrality-dependent distribution. By numerical simulations, it is shown that the network heterogeneity has a influence on the effect of walk preference. In the cascading failure phenomenon, an appropriate degree correlation can guarantee a low risk of cascading failures.     

Lifetime of the two-phonon vibrational state in232Th

We report on a measurement of the lifetime of the 1414 keV state in²³²Th by the Doppler-shift recoil-distance method. This 4⁺ state shows all characteristics of a nearly-harmonic two-phonon-vibrational excitation. The result for the B(E2) value obtained from the lifetime,=3.2 ± 0.7 ps, is in agreement with an earlier estimate of the collectivity from Coulomb-excitation yields and supports the interpretation of the 1414 keV state as a two-phonon-vibrational excitation.We would like to thank the accelerator crew of the Max-Planck-Institut für Kernphysik for the excellent running conditions they maintain. We are also indebted to Dr. H.J. Maier, University Munich for supplying us with the²³²Th targets. This work was supported by the Bundesminister für Forschung und Technologie under contract numbers 06BN601 and 06HD5251.     

Systematic studies of fission fragment kinetic energy distributions by Langevin simulations

Fission fluctuation-dissipation dynamics of heavy nuclei has been studied using Langevin Monte Carlo simulations. The covariant form of the fission transport equation and the coefficients related to it are investigated. To learn about the influence of the dynamics from the ground state to the saddle point on the kinetic energy distributions we have studied various systems and compared the calculations both starting from the ground state and from the saddle point. Both the mean total kinetic energy of the fission fragments and its variances can fit with the experimental values in terms of a finite neck radius as scission condition.This work was supported by the National Natural Science Foundation of China.     

Faddeev–Jackiw canonical path integral quantization for a general scenario,its proper vertices and generating functionals

We generalize the Faddeev–Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.     

Lifetime measurements and particle-rotor calculations for 42 105 Mo63

The half-lives of seven levels in¹⁰⁵Mo have been determined with high precision at the fission-product separator Josef. The-- triple coincidence method with plastic and BaF₂ scintillators was used for a determination of the time between the _q feeding of a level of interest and its depopulation. A value of _q =0.38 (1) for the deformation parameter has been deduced from the half-lives of the first and second excited states. The results of Particle-Rotor model-calculations with the Nilsson parameters=0.084 and=0.28 support the assignment of the Nilsson orbital [532] 5/2^– to the ground state of¹⁰⁵Mo.The authors acknowledge with pleasure fruitful discussions with Profs. W.R. Phillips, I. Ragnarsson and O.W.B. Schult.     

Coherent electromagnetic radiation from the fragments of nuclear fission

The electromagnetic radiation from two vibrating fission fragments is classically treated. The rotational and translational motion of the fragments during emission and the interference of the radiation from the two individual fragments are taken into account. It is shown that the angular distribution of the radiation contains valuable information on the fission process and that the spectral distribution depends sensitively on the damping of the shape vibration.Dedicated to Professor P. Armbruster and P. Kienle on the occasion of their 60th birthday     

On the limits of induced radiation concept in FELs

We discuss a restriction of the induced radiation concept in classical beam systems due to accompanying spontaneous radiation (radiation friction). For short wave FELs, spontaneous radiation renders a noticeable influence on the phasing of particles, which is the base mechanism of induced radiation in classical systems. It leads to an essential restriction on the radiating system length and gain which cannot be compensated by an increase in the beam current. The text was submitted by the authors in English.