Finite times to equipartition in the thermodynamic limit

We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low frequency modes centered at gamma and of width delta-gamma, with both gamma and delta-gamma proportional to N. These initial conditions both give, for finite energy densities E/N, a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density E/N. A theory of the scaling with E/N is presented and compared to the numerical results in the range 0.03 <= E/N <= 0.8.Comment: Plain TeX, 5 `eps' figures, submitted to Phys. Rev.

International R&D Spillovers: A Re-Examination

Coe and Helpman(1995) have measured the extent to which technology spills over between industrialized countries through the particular channel of trade flows. This paper re-examines two particular features of their study. First, we suggest that their functional form of how foreign R&D affects domestic productivity via imports is probably incorrect. We provide an alternative model which turns out to be more accurate, both theoretically and empirically. Second, we take into account two new potential channels of technology transfer: inward FDI and technology sourcing, as proxied by outward FDI. The empirical results show that outward FDI flows and imports flows are two simultaneous channels through which technology is internationally diffused. Inward FDI flows are not a significant channel of technology transfer. The hypothesis of technology sourcing associated with MNEs activities abroad is therefore confirmed while the widespread belief that inward FDI is a major channel of technology transfer is rejected.

Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems

We present evidence that nonlinear resonances govern the tunneling process between symmetry-related islands of regular motion in mixed regular-chaotic systems.In a similar way as for near-integrable tunneling, such resonances induce couplings between regular states within the islands and states that are supported by the chaotic sea. On the basis of this mechanism, we derive a semiclassical expression for the average tunneling rate, which yields good agreement in comparison with the exact quantum tunneling rates calculated for the kicked rotor and the kicked Harper.Comment: 4 pages, 2 figure

Chaos and Energy Redistribution the Nonlinear Interaction of Two Spatio-Temporal Wave Triplets

In this paper we examine the spatio-temporal dynamics of two nonlinearly coupled wave triplets sharing two common modes. Our basic findings are the following. When spatial dependence is absent, the homogeneous manifold so obtained can be chaotic or regular. If chaotic, it drives energy diffusion from long to small wavelengths as soon as inhomogeneous perturbations are added to the system. If regular, one may yet have two distinct cases: (i) energy diffusion is again present if the inhomogeneous modes are linearly unstable and triplets are effectively coupled; (ii) energy diffusion is absent if the inhomogeneous modes are linearly stable or the triplets are uncoupled.Comment: 21 pages, 5 figures, accepted for publication in Physica D (1997

Classical and quantum dynamics of the n-dimensional kicked rotator

The classical and quantum dynamics for an n-dimensional generalization of the kicked planar (n=1) rotator in an additional effective centrifugal potential. Therefore, typical phenomena like the diffusion in classical phase space are similar to that of the one-dimensional model. For the quantum dynamics such a result is not expected as in this case the evolution does depend in a very complicated way on the number n of degrees of freedom. In the limit n --> infinity we find the free undistrubed quantum motion. For finite values of n (1<=n<=26) we study numerically the quantum dynamics. Here, we always find localization independent of the actual number of degrees of freedom.Comment: uuencoded gzipped postscript file, Problem in postscript file resolved. For uncompressed postscript file see http://faupt101.physik.uni-erlangen.de/junker/papers95.ht