Soliton turbulences in the complex Ginzburg-Landau equation

We study spatio-temporal chaos in the complex Ginzburg-Landau equation in parameter regions of weak amplification and viscosity. Turbulent states involving many soliton-like pulses appear in the parameter range, because the complex Ginzburg-Landau equation is close to the nonlinear Schr\"odinger equation. We find that the distributions of amplitude and wavenumber of pulses depend only on the ratio of the two parameters of the amplification and the viscosity. This implies that a one-parameter family of soliton turbulence states characterized by different distributions of the soliton parameters exists continuously around the completely integrable system.Comment: 5 figure

Dynamical scaling and intermittency in shell models of turbulence

We introduce a model for the turbulent energy cascade aimed at studying the effect of dynamical scaling on intermittency. In particular, we show that by slowing down the energy transfer mechanism for fixed energy flux, intermittency decreases and eventually disappears. This result supports the conjecture that intermittency can be observed only if energy is flowing towards faster and faster scales of motion.Comment: 4 pages, 3 figure

On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by `Statistically Preserved Structures' which are associated with exact conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations.Comment: revised version with new data on Navier-Stokes eq

Pairing Matrix Elements and Pairing Gaps with Bare, Effective and Induced Interactions

The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential $v_{low-k}$ is studied in the semiclassical approximation for the case of a typical finite, superfluid nucleus ($^{120}$Sn). It is found that the matrix elements of $v_{low-k}$ follow closely those of $v_{Gogny}$ on a wide range of energy values around the Fermi energy $e_F$, those associated with $v_{low-k}$ being less attractive. This result explains the fact that around $e_F$ the pairing gap $\Delta_{Gogny}$ associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective $k$-mass $m_k\approx 0.7 m$) is a factor of about 2 larger than $\Delta_{low-k}$,being in agreement with $\Delta_{exp}$= 1.4 MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction $v_{ind}$ peaked at $e_F$. The interaction $(v_{low-k}+ v_{ind})Z_{\omega}$ arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion ($\omega-$mass and quasiparticle strength $Z_{\omega}$) due to the particle-vibration coupling leads to a value of the pairing gap at the Fermi energy $\Delta_{ren}$ which accounts for the experimental value

Dissipative quantum dynamics in low-energy collisions of complex nuclei

Model calculations that include the effects of irreversible, environmental couplings on top of a coupled-channels dynamical description of the collision of two complex nuclei are presented. The Liouville-von Neumann equation for the time-evolution of the density matrix of a dissipative system is solved numerically providing a consistent transition from coherent to decoherent (and dissipative) dynamics during the collision. Quantum decoherence and dissipation are clearly manifested in the model calculations. Energy dissipation, due to the irreversible decay of giant-dipole vibrational states of the colliding nuclei, is shown to result in a hindrance of quantum tunneling and fusion.Comment: Accepted in Physical Review

Decay of Quasi-Particle in a Quantum Dot: the role of Energy Resolution

The disintegration of quasiparticle in a quantum dot due to the electron interaction is considered. It was predicted recently that above the energy \eps^{*} = \Delta(g/\ln g)^{1/2} each one particle peak in the spectrum is split into many components ($\Delta$ and $g$ are the one particle level spacing and conductance). We show that the observed value of \eps^{*} should depend on the experimental resolution \delta \eps. In the broad region of variation of \delta \eps the $\ln g$ should be replaced by \ln(\Delta/ g\delta \eps). We also give the arguments against the delocalization transition in the Fock space. Most likely the number of satellite peaks grows continuously with energy, being $\sim 1$ at \eps \sim \eps^{*}, but remains finite at \eps > \eps^{*}. The predicted logarithmic distribution of inter-peak spacings may be used for experimental confirmation of the below-Golden-Rule decay.Comment: 5 pages, REVTEX, 2 eps figures, version accepted for publication in Phys. Rev. Let

Breathing mode in an improved transport approach

The nuclear breathing-mode giant monopole resonance is studied within an improved relativistic Boltzmann-Uehling-Uhlenbeck (BUU) transport approach. As a new feature, the numerical treatment of ground state nuclei and their phase-space evolution is realized with the same semiclassical energy density functional. With this new method a very good stability of ground state nuclei in BUU simulations is achieved. This is important in extracting clear breathing-mode signals for the excitation energy and, in particular, for the lifetime from transport theoretical studies including mean-field and collisional effects.Comment: 33 pages, 11 figures, accepted for publication in Phys. Rev.

The Triaxial Rotation Vibration Model in the Xe-Ba Region

The axial Rotation Vibration Model is here extended to describe also triaxial equilibrium shapes with beta and gamma vibrations allowing for the interaction between vibrations and rotations. This Triaxial Rotation Vibration Model (TRVM) is applied to Xe and Ba isotopes with mass numbers between 120 and 130. This area has recently been pointed out to be the O(6) limit of the Interacting Boson Approximation (IBA). The present work shows that the TRVM can equally well describe these nuclei concerning their excitation energies and E2 branching ratios.Comment: 11 pages, 2 figure

Exact Periodic Solutions of Shells Models of Turbulence

We derive exact analytical solutions of the GOY shell model of turbulence. In the absence of forcing and viscosity we obtain closed form solutions in terms of Jacobi elliptic functions. With three shells the model is integrable. In the case of many shells, we derive exact recursion relations for the amplitudes of the Jacobi functions relating the different shells and we obtain a Kolmogorov solution in the limit of infinitely many shells. For the special case of six and nine shells, these recursions relations are solved giving specific analytic solutions. Some of these solutions are stable whereas others are unstable. All our predictions are substantiated by numerical simulations of the GOY shell model. From these simulations we also identify cases where the models exhibits transitions to chaotic states lying on strange attractors or ergodic energy surfaces.Comment: 25 pages, 7 figure

A note on shell models for MHD Turbulence

We investigate the time evolution of two different (GOY-like) shell models which have been recently proposed to describe the gross features of MHD turbulence. We see that, even if they are formally of the same type sharing with MHD equations quadratic couplings and similar conserved quantities, fundamental differences exist which are related to the ideal invariants.Comment: 6 pages, 5 figures.eps, to appear in Europhysics Letter