Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2009
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/0907.2029 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911256317788160 |
|---|---|
| author | Quintero, Niurka R. Cuesta, Jos'e A. Alvarez-Nodarse, Renato |
| author_facet | Quintero, Niurka R. Cuesta, Jos'e A. Alvarez-Nodarse, Renato |
| contents | Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The bi-harmonic force $f(t)=ε_1\cos(q ωt+ϕ_1)+ε_2\cos(pωt+ϕ_2)$ does it for almost any choice of $ϕ_{1}$ and $ϕ_{2}$, provided $p$ and $q$ are two co-prime integers such that $p+q$ is odd. It has been widely observed, in experiments in Josephson-junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape $v\proptoε_1^pε_2^q\cos(p ϕ_{1} - q ϕ_{2} + θ_0)$ for small amplitudes, where $θ_0$ depends on the damping ($θ_0=π/2$ if there is no damping, and $θ_0=0$ for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0907_2029 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | Symmetries shape the current in ratchets induced by a bi-harmonic force Quintero, Niurka R. Cuesta, Jos'e A. Alvarez-Nodarse, Renato Pattern Formation and Solitons Mathematical Physics Functional Analysis Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The bi-harmonic force $f(t)=ε_1\cos(q ωt+ϕ_1)+ε_2\cos(pωt+ϕ_2)$ does it for almost any choice of $ϕ_{1}$ and $ϕ_{2}$, provided $p$ and $q$ are two co-prime integers such that $p+q$ is odd. It has been widely observed, in experiments in Josephson-junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape $v\proptoε_1^pε_2^q\cos(p ϕ_{1} - q ϕ_{2} + θ_0)$ for small amplitudes, where $θ_0$ depends on the damping ($θ_0=π/2$ if there is no damping, and $θ_0=0$ for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system. |
| title | Symmetries shape the current in ratchets induced by a bi-harmonic force |
| topic | Pattern Formation and Solitons Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/0907.2029 |