10 research outputs found
Instabilities and resistance fluctuations in thin accelerated superconducting rings
The non-equilibrium properties of a driven quasi-one dimensional
superconducting ring subjected to a constant electromotive force ({\it emf}) is
studied. The {\it emf} accelerates the superconducting electrons until the
critical current is reached and a dissipative phase slip occurs that lowers the
current. The phase slip phenomena is examined as a function of the strength of
the {\it emf}, thermal noise, and normal state resistivity. Numerical and
analytic methods are used to make detailed predictions for the magnitude of
phase slips and subsequent dissipation.Comment: Some movies are available here at http://www.lce.hut.fi/~karttune/S
Unstable decay and state selection II
The decay of unstable states when several metastable states are available for
occupation is investigated using path-integral techniques. Specifically, a
method is described which allows the probabilities with which the metastable
states are occupied to be calculated by finding optimal paths, and fluctuations
about them, in the weak noise limit. The method is illustrated on a system
described by two coupled Langevin equations, which are found in the study of
instabilities in fluid dynamics and superconductivity. The problem involves a
subtle interplay between non-linearities and noise, and a naive approximation
scheme which does not take this into account is shown to be unsatisfactory. The
use of optimal paths is briefly reviewed and then applied to finding the
conditional probability of ending up in one of the metastable states, having
begun in the unstable state. There are several aspects of the calculation which
distinguish it from most others involving optimal paths: (i) the paths do not
begin and end on an attractor, and moreover, the final point is to a large
extent arbitrary, (ii) the interplay between the fluctuations and the leading
order contribution are at the heart of the method, and (iii) the final result
involves quantities which are not exponentially small in the noise strength.
This final result, which gives the probability of a particular state being
selected in terms of the parameters of the dynamics, is remarkably simple and
agrees well with the results of numerical simulations. The method should be
applicable to similar problems in a number of other areas such as state
selection in lasers, activationless chemical reactions and population dynamics
in fluctuating environments.Comment: 28 pages, 6 figures. Accepted for publication in Phys. Rev.
Unstable decay and state selection
We consider the problem of state selection for a stochastic system, initially
in an unstable stationary state, when multiple metastable states compete for
occupation. Using path-integral techniques we derive remarkably simple and
accurate formulas for state-selection probabilities. The method is sufficiently
general that it is applicable to a wide variety of problems.Comment: 4 pages, 2 figure