Sensitive Method for the Measurement of Nonlinearity of Electrical Conduction

Skov, Charles E.; Pearlstein, Edgar

doi:10.1063/1.1718961

Cited by 15 publications

(7 citation statements)

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“…In contrast, if p and q have different parity, shift symmetry is broken by f (t) so the force can induce a nonzero net current [23]. Many attempts have been made to determine quantitatively the dependence of the ratchet velocity, v, on the parameters of the bi-harmonic force (1) [11,24,25]. Invariably, the analysis performed in these works rests on the so-called method of moments, where it is assumed that the average ratchet velocity can be expanded as a series of the odd…”

Section: Introductionmentioning

confidence: 99%

Ratchet effect on a relativistic particle driven by external forces

Quintero

Álvarez-Nodarse

Cuesta

2011

J. Phys. A: Math. Theor.

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We study the ratchet effect of a damped relativistic particle driven by both asymmetric temporal bi-harmonic and time-periodic piecewise constant forces. This system can be formally solved for any external force, providing the ratchet velocity as a non-linear functional of the driving force. This allows us to explicitly illustrate the functional Taylor expansion formalism recently proposed for this kind of systems. The Taylor expansion reveals particularly useful to obtain the shape of the current when the force is periodic, piecewise constant. We also illustrate the somewhat counterintuitive effect that introducing damping may induce a ratchet effect. When the force is symmetric under time-reversal and the system is undamped, under symmetry principles no ratchet effect is possible. In this situation increasing damping generates a ratchet current which, upon increasing the damping coefficient eventually reaches a maximum and decreases toward zero. We argue that this effect is not specific of this example and should appear in any ratchet system with tunable damping driven by a time-reversible external force. PACS numbers:Submitted to: J. Phys. A: Math. Gen.

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Section: Introductionmentioning

confidence: 99%

Ratchet effect on a relativistic particle driven by external forces

Quintero

Álvarez-Nodarse

Cuesta

2011

J. Phys. A: Math. Theor.

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“…A big deal of simulations and experiments have show [2,4,5,7,8,11,[20][21][22][23][24][25][26][27] that in many different systems the behavior of the ratchet velocity v driven by the T -periodic bi-harmonic force (1) where T = 2π/ω, φ 1 and φ 2 are the phases, p and q are co-primes with p + q odd, and the amplitudes ǫ 1 and ǫ 2 are small, is given by the expression…”

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confidence: 99%

Symmetries shape the current in ratchets induced by a biharmonic driving force

2010

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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 biharmonic force f͑t͒ = ⑀ 1 cos͑qt + 1 ͒ + ⑀ 2 cos͑pt + 2 ͒ does it for almost any choice of 1 and 2 , provided p and q are two coprime integers such that p + q is odd. It has been widely observed, in experiments in semiconductors, in Josephson junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape v ϰ ⑀ 1 p ⑀ 2 q cos͑p 1 − q 2 + 0 ͒ for small amplitudes, where 0 depends on the damping ͑ 0 = / 2 if there is no damping, and 0 = 0 for overdamped systems͒. 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. Ratchetlike transport phenomena, where a net motion of particles or solitons is induced by zero-average forces, can be observed in many physical systems. Such is, for instance, the dc current in semiconductors ͓1-3͔, the net motion of fluxons in long Josephson junctions ͑JJs͒ ͓4,5͔, of vortices in superconductors ͓6͔, of cold atoms in optical lattices ͓7,8͔, or the rectification of Brownian motion ͓9-11͔. In some of these systems, the ratchetlike motion is induced by means of spatial asymmetries ͓12,13͔. In the others the transport can also appear if some temporal symmetries are broken by timedependent forces, e.g., ͓13-18͔. This latter case has two advantages: it is generally easier to analyze theoretically, and it is more amenable to experimental observation, e.g., in semiconductors ͓2͔, in JJs ͓4,5͔, or in optical lattices ͓8,19͔.A large number of simulations and experiments have show ͓2,4,5,7,8,11,20-27͔ that in many different systems the behavior of the ratchet velocity v driven by the T-periodic biharmonic forcewhere T =2 / , 1 and 2 are the phases, p and q are coprimes with p + q odd, and the amplitudes ⑀ 1 and ⑀ 2 are small, is given by the expressionwhere B and 0 depend on the parameters of the model and on but neither on the amplitudes nor on the phases ͓4,8,17,19,22,23,26͔. It has also been shown for specific systems that nondissipative dynamics have 0 = / 2 ͓7,15͔, whereas overdamped ones have 0 =0 ͓5,21,27͔. The aim of this Rapid Communication is to show that symmetry considerations alone are enough to predict behavior ͑2͒. This is a strong result because it is valid for any equation that describes the system, no matter the type of nonlinear terms it may contain, as long as it shows invariance under certain symmetry transformations-which will state precisely below. Attempts at determining the shape of current ͑2͒ can be found even in the pioneering works ͓2,20͔, aimed at developing a sensitive method of measuring deviations from Ohm's law. Their analysis, however, relies on an expansion of v in odd moments of f͑t͒, justified by the...

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“…It was Rosenblat [1] who first at the end of 40th suggested that the dc component of electric or magnetic field may arise in pure ac-driven electrical circuits with nonlinear and symmetric characteristics. A similar idea has been proposed by Skov and Pearlstein in the middle of 60th [2]. Soon after these theoretical predictions, the DC due to mixing of ac electric field and its second harmonic has been observed for the warm electrons in germanium by Pozhela and Karlin [3], and, independently, by Schneider and Seeger [4].…”

Section: Introductionsupporting

confidence: 55%

Direct current generation due to wave mixing in semiconductor superlattices

Alekseev

Kusmartsev²

Conference Digest. 2000 International Quantum Electronics Conference (Cat. No.00TH8504)

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We discuss an effect of dc current and dc voltage (stopping bias) generation in a semiconductor superlattice subjected by an ac electric field and its phase-shifted n-th harmonic. In the low field limit, we find a simple dependence of dc voltage on a strength, frequency, and relative phase of mixing harmonics for an arbitrary even value of n.We show that the generated dc voltage has a maximum when a frequency of ac field is of the order of a scattering constant of electrons in a superlattice. This means that for typical semiconductor superlattices at room temperature operating in the THz frequency domain the effect is really observable. Indeed, such conditions are most used in the modern experiments on THz harmonics generation in superlattices.We also made a comparison of a recent paper describing an effect of a directed current generation in a semiconductor superlattice subjected by ac field and its second harmonic (n = 2) [K. Seeger, Appl. Phys. Lett. 76, 82 (2000)] with our earlier findings describing the same effect [K. Alekseev et al., Europhys. Lett. 47, 595 (1999); cond-mat/9903092]. In particular, here we found that the maximum value of dc current is associated with the THz domain that also follows from Seeger's calculations. This maximum value has already been highlighted in our previous work.For the mixing of an ac field and its n-th harmonic with n ≥ 4, we found that additionally to the phase-shift controlling of the dc current, there is a frequency control. This frequency controlling of the dc current direction is absent in the case of n = 2. The found effect is that, both the dc current suppression and the dc current reversals exist for some particular values of ac field frequency. For typical semiconductor superlattices such an interesting behavior of the dc current should be observable also in the THz domain.Finally, we briefly review the history of the problem of the dc current generation at mixing of harmonics associated with arbitrary coherent electromagnetic waves in semiconductors and semiconductor microstructures.

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Sensitive Method for the Measurement of Nonlinearity of Electrical Conduction

Cited by 15 publications

References 1 publication

Ratchet effect on a relativistic particle driven by external forces

Ratchet effect on a relativistic particle driven by external forces

Symmetries shape the current in ratchets induced by a biharmonic driving force

Direct current generation due to wave mixing in semiconductor superlattices

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