Symmetries shape the current in ratchets induced by a bi-harmonic force

Abstract

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 $f(t)={\epsilon }_1\cos (q\omega t+{\varphi }_1)+{\epsilon }_2\cos (p\omega t+{\varphi }_2)$ does it for almost any choice of ${\varphi }_1$ and ${\varphi }_2$, 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 $v\propto {\epsilon }_1^p{\epsilon }_2^q\cos (p{\varphi }_1-q{\varphi }_2+{\theta }_0)$ for small amplitudes, where ${\theta }_0$ depends on the damping (${\theta }_0=\pi /2$ if there is no damping, and ${\theta }_0=0$ 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.

4 pages

References in corpus (1)

• Optical ratchets with discrete cavity solitons

Cited by in corpus (23)

• Driving magnetic skyrmions with microwave fields
• Current reversals in a rocking ratchet: dynamical vs symmetry-breaking mechanisms
• Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force
• Skyrmion ratchet effect driven by a biharmonic force
• Current reversals in a rocking ratchet: the frequency domain
• Transport driven by biharmonic forces: impact of correlated thermal noise
• Time-shift invariance determines the functional shape of the current in dissipative rocking ratchets
• Irrationality and quasiperiodicity in driven nonlinear systems
• Control of transport in higher dimensional systems via dynamical decoupling of degrees of freedom with quasiperiodic driving fields
• Directed Ratchet Transport in Granular Crystals
• Analysis of interface conversion processes of ballistic and diffusive motion in driven superlattices
• Ratchet universality in the presence of thermal noise
• Disorder-induced regular dynamics in oscillating lattices
• Non-sinusoidal current and current reversals in a gating ratchet
• Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing
• Two coupled Josephson junctions: dc voltage controlled by biharmonic current
• External field-induced dynamics of a charged particle on a closed helix
• Directed motion of domain walls in biaxial ferromagnets under the influence of periodic external magnetic fields
• Ratchet effect on a relativistic particle driven by external forces
• Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model
• The transport phenomenon of inertia Brownian particles in a periodic potential with non-Gaussian noise
• Comment on "Ratchet universality in the presence of thermal noise"
• Universal patterns in multifrequency-driven dissipative systems