Kramers Escape Research Articles

Fluctuations of critical current and phase slippage in Josephson junctions.

The effect of critical current noise on the phase-slip- rate in an overdamped Josephson junction is calculated. A significant increase of the Kramers escape rate is predicted for submicron metal-insulator-metal junctions. The temperature dependence of the rate shows deviations from the Arrhenius law at low temperatures if the junction conductance fluctuations are produced by quantum ionic tunneling processes in the junction barrier. Implications for magnetization decay in high-${T}_{c}$ superconductors are discussed.

Escape times in interacting biased random walks

The dynamics ofN particles with hard core exclusion performing biased random walks is studied on a one-dimensional lattice with a reflecting wall. The bias is toward the wall and the particles are placed initially on theN sites of the lattice closest to the wall. ForN=1 the leading behavior of the first passage timeT FP to a distant sitel is known to follow the Kramers escape time formulaT FP∼λ l whereλ is the ratio of hopping rates toward and away from the wall. ForN > 1 Monte Carlo and analytical results are presented to show that for the particle closest to the wall, the Kramers formula generalizes toT FR∼λ IN. First passage times for the other particles are studied as well. A second question that is studied pertains to survival timesT s in the presence of an absorbing barrier placed at sitel. In contrast to the first passage time, it is found thatT s follows the leading behaviorλ′ independent ofN.