1. Spontaneous current induced by symmetry breaking in coupled oscillators NSPCS 1-4 July 2008 KIAS, Korea Fabio Marchesoni 1 / Hyunggyu Park 2 1 Universita di Camerino, Italy 2 Korea Institute for Advanced Study Hyunsuk Hong Chonbuk National University

2. Introduction What induces the current? What mechanism? Recently, it has been reported that nonzero current is induced in the system of coupled units. Is the thermal noise essential to induce the current? Any relation between the nonzero current and synchronization? Mechanism is not clearly known yet Furthermore, it has been known that thermal noise is important to induce the current.

3. Model: intrinsic frequency phase of the i-th oscillator coupling strength System of coupled oscillators with a pinning force “pinning force” Local potential: For a>2b,For a<2b, “global coupling”

4. Introducing the synchronization order parameter Oscillators: static oscillators + dynamic oscillators

5. symmetry broken symmetry increasing dynamic oscillator: static oscillator: increasing

6. Order parameter : Imaginary part of synchronization order parameter We expect

7. Numerical Results for all Always synchronized Transition at

8. Self-consistency equation : static oscillator group Critical condition for the transition:

9. Phase diagram “reentrant transition” by ? window closing

10. increasing Any contribution from the dynamic oscillators? Symmetry breaking in static oscillators Symmetry breaking in dynamic oscillators Current So far, we have focussed on the static oscillators

11. Phase velocity mismatch andFor (Kuramoto model) mismatch

12. Summary and outlook But, we found that it is NOT essential term to induce the current. In many previous studies, it has been reported that thermal noise is important and essential to induce the current. In one recent study, the system with thermal noise has been studied: J. Buceta et. al, Phys. Rev. E 61, 6287 (2000) We found that spontaneous current can be induced even in the case of fully deterministic system. Our model is simple Detail analytic approach is available, yielding deeper understanding Symmetry breaking in the static oscillator Symmetry breaking in the dynamic oscillators SPONTANEOUS CURRENT ! Phase diagram, “reentrant transition” We have a plan to extend the study to the low-dimensional system with nearest neighbor coupling