Distribution of the widths of resonances for strong overlap and numerous decay channels: Influence on the average survival probability

Desouter-Lecomte, M.; Culot, F.
May 1993
Journal of Chemical Physics;5/15/1993, Vol. 98 Issue 10, p7819
Academic Journal
The distribution of the widths of N quasidegenerate metastable states decaying into a large number K of dissociation continua is studied in the framework of the random matrix theory. For strong overlap, the distribution of the imaginary parts of the eigenvalues of the effective Hamiltonian H-iΓ/2 is that of the eigenvalues of the width matrix Γ. The latter is found to belong to a model of random matrices proposed by Wigner and developed by Dyson. The analytical expression of the asymptotic density ρ(γ) for equal partial widths and N=K→∞ is a semicircular law centered at twice the mean width γ times a function 1/γ. It predicts extensive fluctuations around the mean with a high density of small widths. As a result, the average survival probability of the metastable states lying within a narrow energy range decays more slowly than the exponential law which is assumed in the RRKM theory.


Related Articles

  • Concentration fluctuations in fluid mixtures. Mazo, Robert M. // Journal of Chemical Physics;10/21/2008, Vol. 129 Issue 15, p154101 

    The B matrix of the Kirkwood–Buff theory of solutions describes number fluctuations of the component species. We show how, when the eigenvalues of the B matrix are widely different in magnitude, the description of the fluctuations can be simplified by restriction to a lower dimensional...

  • Robust Evolutionary Approach to Mitigate Low Frequency Oscillation in a Multi-machine Environment. Mazlumi, K.; Azari, M. // International Journal on Electrical & Power Engineering;Nov2013, Vol. 4 Issue 3, p18 

    This paper proposes a new optimization algorithm known as Modified Shuffled Frog Leaping Algorithm (MSFLA) for optimal designing of PSSs controller. The design problem of the proposed controller is formulated as an optimization problem and MSFLA is employed to search for optimal controller...

  • CONTINUOUS PRECIPITATION: A MODEL BASED STABILITY ANALYSIS. BOTOND, SZILÁGYI; RÉKA, BARABÁS // Studia Universitatis Babes-Bolyai, Chemia;Sep2013, Vol. 58 Issue 3, p155 

    In the current study a model based stability analysis of a continuous mixed suspension mixed product removal crystallizer, widely used in pilot and industrial scale, is investigated. The population balance approach is used to model the size distribution of solid particulate phase, taking into...

  • Capillary oscillations of a constrained liquid drop. Bostwick, J. B.; Steen, P. H. // Physics of Fluids;Mar2009, Vol. 21 Issue 3, p032108 

    An inviscid spherical liquid drop held by surface tension exhibits linear oscillations of a characteristic frequency and mode shape (Rayleigh oscillations). If the drop is pinned on a circle of contact the mode shapes change and the frequencies are shifted. The linear problem of inviscid,...

  • Determination of the reduced range of frequencies and forms of free fluctuations of systems with large number of degrees of freedom on the basis of spline collocation condensation. Ignatev, V. A.; Romashkin, V. N. // Vestnik Volgogradskogo Gosudarstvennogo Arhitekturno-Stroitelnog;2014, Vol. 35 Issue 54, p140 

    The authors presented a modified version of the static condensation method to solve the incomplete algebraic eigenvectors and eigenvalues problem for systems with many degrees of freedom. Its essence is to use a spline interpolation of the function of displacement in the range between the...

  • A fluctuation removal based univariate integration over prescribed nodes. Kurşunlu, Ayşegül; Demiralp, Metin // Journal of Mathematical Chemistry;Feb2011, Vol. 49 Issue 2, p428 

    This work aims at the evaluation of a univariate integral based on one node fluctuation free integration and by using exponential weight function. This is the companion of a paper presenting fundamental aspects of one node integration. In contrast to companion paper, this paper deals with more...

  • Existence of Purely Imaginary Eigenvalues for DAEs with Network Structure. Riaza, Ricardo; Tischendorf, Caren // AIP Conference Proceedings;9/30/2010, Vol. 1281 Issue 1, p1000 

    We present a qualitative eigenvalue analysis of differential algebraic equations with a certain structure. The structure refers to hybrid modells of linear dynamic networks. In particular, we present a characterization for the existence of purely imaginary eigenvalues. This qualitative question...

  • Fluctuations of the One-Dimensional Polynuclear Growth Model in Half-Space. Sasamoto, T.; Imamura, T. // Journal of Statistical Physics;May2004, Vol. 115 Issue 3/4, p749 

    We consider the multi-point equal time height fluctuations of the one-dimensional polynuclear growth model in half-space. For special values of the nucleation rate at the origin, the multi-layer version of the model is reduced to a process with a determinantal weight, for which the asymptotics...

  • Asymptotic Resonance, Interaction of Modes and Subharmonic Bifurcation. Molteni, Giuseppe; Serra, Enrico; Tarallo, Massimo; Terracini, Susanna; Stuart, C. A. // Archive for Rational Mechanics & Analysis;Oct2006, Vol. 182 Issue 1, p77 

    We study the existence of small amplitude oscillations near elliptic equilibria of autonomous systems, which mix different normal modes. The reference problem is the Fermi-Pasta-Ulam β-model: a chain of nonlinear oscillators with nearest-neighborhood interaction. We develop a new bifurcation...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics