# Graduate School in Nonlinear Science

### Sponsored by the Danish Research Academy

**
MIDIT OFD CATS
Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies
and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and
Technical University of Denmark Building 128 Department of Chemistry
Building 321 P.O. Box 49 University of Copenhagen
DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø
Denmark Denmark Denmark
**

**THE INVERSE JOSEPHSON EFFECT IN CONTINUOUS AND DISCRETE JUNCTIONS**

by** Giovanni Filatrella**

Physics Department

University of Salerno, Italy

MIDIT-seminar 441

**Monday February 15, 1999, 15.15 h**

at MIDIT, IMM Building 305, room 027

**Abstract**: The inverse ac Josephson effect involves
rf-induced (Shapiro) steps,
i.e. the appearance of a dc voltage on the IV characteristic due to an
ac drive. The standard analysis for small junctions yields a well
known Bessel function dependence on the effective drive
amplitude. A more recent approach, using a first order
power-balance approach has allowed the extension of the
threshold analysis of the so called zero-crossing steps (the steps
that cross the zero current axis) also for low voltage values, while it
converges to the traditional one for high voltage values.
The power
balance approach has proved very useful also for
continuous modulated long Josephson junctions, which is well described
by a perturbed sine-Gordon equation. In this case one can show that a
pure ac bias current can drive a kink (in the language of josephson
junctions, the fluxons) at a resonant mean velocity. Moreover, the
theory can be extended also to predict the extension of the steps.
Finally, we have numerically proved that in the corresponding
discrete system, a lattice of the Krenkel-Kontorova type, one can
eliminate the inhomogeneities because the periodic potential
is given by the effective Peierls-Nabarro potential induced by the
discreteness. The features of this effects have just been numerically
grasped by numerical simulations, but a complete theoretical framework
is still lacking.