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

Do Directors Have a Use-By Date? Examining the Impact of Board Tenure on Firm Performance

Corporate boards serve the dual important functions of monitoring and advising management. We examine whether corporate boards consisting of longer-serving independent directors are better able to fulfill these functions due to firm-specific knowledge accumulation, or whether director performance suffers due to declining effectiveness in monitoring managers and/or overall staleness of board capital (board value to shareholders). Using a broad sample of up to 3,800 firms over a 20-year period, our evidence suggests that board tenure is positively related to forward-looking measures of market value and stock returns, with the relationship reversing after about nine years on average. The detrimental effect of longer average board tenure on market value (after an initial period of positive effects) is stronger for high growth firms, which is consistent with the deterioration of the board members’ ability to perform their advisory function

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.

Nonequilibrium properties of mesoscopic superconducting rings

In this thesis we study certain nonequilibrium properties of mesoscopic superconducting rings, i.e., rings of finite circumference. Two classes of nonequilibrium behavior will be considered: (i) the system is prepared in a nonequilibrium state and subsequently allowed to relax toward equilibrium, and (ii) the the system in contact with an external driving force that does not allow the system to relax toward equilibrium.In Chap. 2 we consider the problem of the decay rate of a persistent supercurrent. For the case of wires that are in the thermodynamic limit (i.e., not mesoscopic) the temperature and current dependence of the persistent-current lifetimes has been calculated. In this thesis we extend these results to include the dependence of the lifetime on the length of the wire. We find that as the length of the wire is reduced, the rate of decay, per unit length of the wire, decreases.Our calculation of the length-dependence of the lifetime of a persistent current enables a comparison of two distinct experimental configurations: the superconductor is driven by (i) a voltage source, and by (ii) a current source. We find that for systems driven by a voltage source, the length-dependent corrections to the lifetime of a current-carrying state are substantial, whereas, for the case of a current source, the lifetime does not acquire any substantial length-dependent corrections. This is an explicit example of the general result that for mesoscopic systems, i.e., systems that are not in the thermodynamic limit, the choice of the ensemble is not free.In order to calculate the lifetime of a persistent current, it is necessary to compute the ratio of determinants of differential operators, with all zero eigenvalues omitted. The process of factoring out the zero eigenvalues is known as regularization. The powerful formalism that has been developed for computing the determinants of differential operators including all of the eigenvalues (i.e., unregularized determinants), is extended to allow for computation of the regularized determinants in a form that is no more complicated than the computation of the unregularized determinant.Finally, we study the dynamics of the supercurrent near the critical supercurrent. We imagine that the ring is under the influence of an electric field of sufficient strength so that the current can be driven to the critical current, at which point the system becomes unstable. We find that for 'weak' electric fields, single phase-slip processes dominate, but as the field strength is increased there is a crossover to double phase-slip dominated behavior. These results lead us to consider the general problem of the decay from an unstable state when multiple metastable states compete for occupation. We present a possible approach, inspired by the Onsager-Machlup formalism and based on a path integral technique, to this problem

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