Stafford, and DLS,inNoise in Complex Systems and Stochastic Dynamics II(SPIE Proceedings Series 5471, 2004), pp. Thermal fluctuations responsible for nucleating changes in radius 0 J._ Treat radius fluctuations as a classical field φ(z,t) on : R(z,t) = R0 + φ(z,t) _ Fluctuations occur in potential _ Escape rate calculable from Kramers theory: G = G exp Model of nanowire `decay’ rate This is essentially the same procedure as computing quantum corrections about the classical path in the Feynman path-integral approach to quantum mechanics. To compute the prefactor G0, must examine fluctuations about the optimal escape (classical) path. Need to study extrema of the action, which are solutions of the nonlinear ODE Uniform solutions: Nonuniform (bounce*) solutions: * Or critical dropletīut: how do we know which is the true saddle configuration? Ans: the saddle is the lowest energy configuration with a single unstable direction. The infinite line case (Langer `69, Callan-Coleman ’77) Let Then the stable, unstable, and saddle states are time-independent solutions of the zero-noise GL equation: That is, the states that determine the transition rates are extrema of the action. 91, 254501 (2003).īecause the zero-noise dynamics are gradient, where Consider an extended system with gradient dynamics perturbed by weak spatiotemporal white noise, for example the stochastic Ginzburg-Landau equation: Theoretical stability diagram But: why should these wires exist at all? Rayleigh instability: cylindrical column of fluid held together by pairwise interactions is unstable to breakup by surface wavesĮlectron Shell Potential J. Why nanowires? Moore’s law International Technology Roadmap for Semiconductors: 1999 Extrapolates to 1nm technology by 2020Ĭ.-H. Experimental Evidence for the Phase Transition?.Magnetization Reversal in Quasi-2D Nanomagnets.Classical Activationin Stochastic Field Theories.Decay of monovalent metallic nanowires.Partially supported by US National Science Foundation Grants PHY009484, PHY0351964, and PHY0601179 Large Fluctuations, Classical Activation, Quantum Tunneling, and Phase Transitions Daniel Stein Departments of Physics and Mathematics New York University Conference on Large Deviations: Theory and Applications University of Michigan June 4-8, 2007 Collaborators: Jerome Bürki (Physics, Arizona), Andy Kent (Physics, NYU), Robert Maier (Math, Arizona),Kirsten Martens (Physics, Heidelberg), Charles Stafford (Physics, Arizona) Reference: DLS, Braz.
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