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We study the systematics of the giant dipole resonance width Γ in hot rotating nuclei as a function of temperature T , spin J and mass A. We compare available experimental results with theoretical calculations that include thermal shape fluctuations in nuclei ranging from A = 45 to A = 208. Using the appropriate scaled variables, we find a simple phenomenological function Γ(A, T, J) which approximates the global behavior of the giant dipole resonance width in the liquid drop model. We reanalyze recent experimental and theoretical results for the resonance width in Sn isotopes and 208 Pb.PACS numbers: 05.45.+b, 21.60.Fw, Hot rotating nuclei are usually produced in heavy ion fusion reactions through transfer of the energy and angular momentum of the relative motion into internal degrees of freedom. The resulting hot nucleus can decay through particle and gamma-ray emission. From the decay patterns of these nuclei one can hope to understand their properties under extreme conditions such as high temperature and spin. A particularly useful experimental probe in the study of hot nuclei has been the giant dipole resonance (GDR) [1,2]. At zero temperature, the GDR vibrational frequency is inversely proportional to the length of the axis along which the vibration occurs, and the quadrupole deformation of the nucleus can be inferred from the splitting of the GDR peak. At finite temperature the nuclear shape fluctuates, and the relationship between the shape and the observed resonance properties is more complex. In the adiabatic limit the observed GDR strength function is calculated through an average over a thermal ensemble of shapes corresponding to all quadrupole degrees of freedom [3]. These include both the intrinsic shape and the nuclear orientation with respect to its rotation axis. The fluctuation theory explains successfully both the observed cross-section and angular anisotropy of the GDR radiation [4][5][6].In recent years, a wealth of experimental results for the GDR has become available in wider regions of temperature and spin [6][7][8][9]. In the fusion experiments, higher excitation energies are usually accompanied by larger amounts of angular momentum transfer. However, in recent inelastic scattering experiments of light particles (e.g. alpha particles) from heavy nuclei the GDR could be excited over a range of temperatures without substantial angular momentum transfer [9]. Although detailed theoretical analyses of the GDR have been done in many nuclei, a comprehensive study of its global features has been lacking. In this letter we present a systematic analysis of the GDR width as a function of temperature T , spin J and mass A. We compare available experimental results with theoretical calculations in nuclei ranging from A ∼ 45 to A ∼ 208. The calculations include thermal shape fluctuations using both Nilsson-Strutinsky (NS) and liquid drop (LD) free energy surfaces. We find that by introducing appropriate scaling of the variables it is possible to approximate the GDR width Γ(A, T, J) in the LD regime by a...

Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We find that the reduced density matrix can display dynamics given by Lévy stable laws. The classical limit of these dynamics can be related to fractional kinetic equations. In particular we derive a fractional extension of Kramers equation.PACS numbers: 05.40.+j, 02.50.-r, 05.30.-d, 05.45.+b Whether one studies deterministic Hamiltonian or dissipative systems, one finds that transport in chaotic systems often resembles some type of stochastic process. The dynamics of such systems leads to a rich spectrum of behaviors, from enhanced diffusion such as tracer diffusion in flows and turbulent diffusion in the atmosphere, to dispersive diffusion [1]. Much effort has been spent in recent years to understand such classical stochastic processes in chaotic systems, leading to the development of approaches ranging from fractional kinetic equations [2-4], Lévy flights [5] to random walks in random environments [5,6] and stochastic webs [7]. One of the common features to all of these is the use of Lévy stable laws [8]. It was shown by Lévy [9], in studies of extensions of the central limit theorem, that a continuous class of nongaussian processes satisfy the same fundamental equation that gives rise to the theory of gaussian processes, namely the Chapman-Kolmogorov equation for the conditional probability P (q, q ′ , t):The standard solution, P (q, q ′ , t) = exp(−(q − q ′ ) 2 /4Dt)/(4πDt) 3/2 , gives rise to the gaussian processes and the usual form of the Fokker-Planck equation. The general solutions of Lévy provide a way to generalize Brownian motion. The non-gaussian processes which satisfy (1) are known as Lévy stable laws, and have the form:where 0 < α ≤ 2 and A ∝ t. The case α = 2 corresponds to gaussian processes. The Lévy distributions L A α (q) satisfy the scaling relation:where for A = 1 we drop the superscript: L 1 α (x) = L α (x). For α < 2, these distributions are characterized by infinite second moments, as one can easily infer from the asymptotic behavior for q → ±∞ [5],These non-gaussian processes can be related to anomalous transport in a variety of (classical) physical systems [6], as well as to classically chaotic systems. We have recently shown that turbulent diffusion can also arise in the time evolution of complex quantum systems [10]. Here we find that a general form of quantum chaotic backgrounds can give rise to quantum evolution characterized by Lévy distributions. Further, we can connect, in the semi-classical limit, such processes to fractional kinetic theory, which was initially introduced as a phenomenological approach to classical anomalous diffusion.We would like to study the problem of a particle coupled to a chaotic environment, quantum mechanically. It has been realized in recent years that the quantum counterpart of chaos is random matrix theory. For ...

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