Deterministic ratchets: Route to diffusive transport

Borromeo, M.; Costantini, Giulio; Marchesoni, F.

doi:10.1103/physreve.65.041110

Cited by 62 publications

(57 citation statements)

References 23 publications

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“…The development of theoretical and computational models of ratchet systems flourishes [35][36][37][38][39][40][41][42][43][44] and is essential for the design of new separation methods and the interpretation of experimental observations. One of the challenges encountered in describing the operation of real electrophoresis-based ratchets is the faithful representation of the field lines in microfabricated electrophoretic devices.…”

Section: Ratchetsmentioning

confidence: 99%

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

et al. 2002

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Over the last two decades, the introduction of new methods such as pulsed-field gel electrophoresis and capillary array electrophoresis has made it possible to map and sequence entire genomes, including our own. The development of these experimental methods has been helped by the progress of theoretical and computational sciences, and the interactions between these three modi operandi of modern science are still pushing the limits of our technologies. We now see a clear trend towards proteomics and microfluidic (even nanofluidic!) devices. In this review, we take a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts. About a dozen different subfields are discussed and reviewed. We conclude by giving a commented list of some of the best review articles published over the last 2-3 years.

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Section: Ratchetsmentioning

confidence: 99%

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

et al. 2002

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“…Such an approximation essentially treats the vortex as a rigid object, and its dynamics can be reduced to the dynamics of a relativistic underdamped point-like particle [7] (cf. non-relativistic case [17]). In this terms the ratchet should rectify ξ(t) to produce a nonzero average velocity u = 0.…”

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High-Efficiency Deterministic Josephson Vortex Ratchet

et al. 2005

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We investigate experimentally a Josephson vortex ratchet -a fluxon in an asymmetric periodic potential driven by a deterministic force with zero time average. The highly asymmetric periodic potential is created in an underdamped annular long Josephson junction by means of a current injector providing efficiency of the device up to 91%. We measured the ratchet effect for driving forces with different spectral content. For monochromatic high-frequency drive the rectified voltage becomes quantized. At high driving frequencies we also observe chaos, sub-harmonic dynamics and voltage reversal due to the inertial mass of a fluxon. The ratchet effect, i.e., the net unidirectional motion of a particle in a spatially asymmetric periodic potential in the presence of deterministic or stochastic forces with zero time average, received a lot of attention during the 20-th century. The second law of thermodynamics does not allow to extract useful work out of equilibrium thermal fluctuations, as was didactically demonstrated by Feynman [1]. Thus, the only way to produce useful work is to supply non-native fluctuations (usually colored noise), which is the basic principle of operation for any ratchet.Particularly during the last decade ratchets were receiving a lot of attention [2,3,4]. Several new implementations, in particular based on the motion of the Josephson phase in SQUIDs [5] or vortices in long Josephson junctions (LJJ) [6,7,8,9] or Josephson junction arrays (JJA) [10,11,12], were suggested and tested. The investigation of quantum ratchets [13,14,15], i.e., a quantum particle moving/tunneling quantum mechanically in an asymmetric potential, is a fascinating new field not very well developed up to now especially experimentally. Advantages of Josephson junction based ratchets are: (I) directed motion results in an average dc voltage which is easily detected experimentally; (II) Josephson junctions are very fast devices which can operate (capture and rectify noise) in a broad frequency range from dc to ∼ 100 GHz, thus capturing a lot of spectral energy; (III) by varying junction design and bath temperature both overdamped and underdamped regimes are accessible; and (IV) one can operate Josephson ratchets in the quantum regime [15].In this letter we investigate experimentally the deterministic underdamped Josephson vortex ratchet (JVR), in which a Josephson vortex (fluxon) moves along a LJJ. We implemented a novel, effective way to construct a strongly asymmetric potential by means of a current injector and systematically study a quasi-statically driven ratchet with different spectral content of the driver. For non-adiabatic drive we observe quantized rectification, voltage reversal, sub-harmonic, and chaotic dynamics. Our system can be described by the following perturbed sine-Gordon equation [6] φwhere φ is the Josephson phase, the curvilinear coordinate x along the LJJ and the time t are normalized to the Josephson penetration depth λ J and inverse plasma frequency ω −1 p , accordingly, α is the dimensionless damping pa...

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“…An important class of ratchets is given by the rocking ratchet, characterized by a time-independent potential and an external perturbation (driving force) which may be either deterministic or stochastic, or a combination of both. [3,4,5,6,7] The number of ratchet systems considered for experimental studies has steadily been growing during recent years.[2] In particular, superconducting ratchets, based on the motion of Abrikosov vortices [8,9,10,11,12], Josephson vortices [13,14,15,16,17] or the phase difference of the superconducting wavefunction (Josephson phase) in SQUID ratchets [18,19,20,21] have been investigated. Those systems offer the advantage of (i) good experimental control over externally applied driving forces (here: currents), (ii) easy detection of directed motion, which creates a dc voltage, and (iii) experimental access to studies over a wide frequency range of external perturbations (adiabatic and non-adiabatic regime), and transition from overdamped to underdamped dynamic regimes, enabling studies of inertial effects and transition to chaos.…”

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Three-Junction SQUID Rocking Ratchet

2005

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We investigate 3-junction SQUIDs which show voltage rectification if biased with an ac current drive with zero mean value. The Josephson phase across the SQUID experiences an effective ratchet potential, and the device acts as an efficient rocking ratchet, as demonstrated experimentally for adiabatic and nonadiabatic drive frequencies. For high-frequency drives the rectified voltage is quantized due to synchronization of the phase dynamics with the external drive. The experimental data are in excellent agreement with numerical simulations including thermal fluctuations.PACS numbers: 74.40.+k, 85.25.Dq During the last decade, directed molecular motion in the absence of a directed net driving force or temperature gradient in biological systems has drawn much attention to Brownian motors.[1, 2] Nonequilibrium fluctuations can induce e.g. transport of particles along periodic structures which lack reflection symmetry -socalled ratchets. An important class of ratchets is given by the rocking ratchet, characterized by a time-independent potential and an external perturbation (driving force) which may be either deterministic or stochastic, or a combination of both. [3,4,5,6,7] The number of ratchet systems considered for experimental studies has steadily been growing during recent years.[2] In particular, superconducting ratchets, based on the motion of Abrikosov vortices [8,9,10,11,12], Josephson vortices [13,14,15,16,17] or the phase difference of the superconducting wavefunction (Josephson phase) in SQUID ratchets [18,19,20,21] have been investigated. Those systems offer the advantage of (i) good experimental control over externally applied driving forces (here: currents), (ii) easy detection of directed motion, which creates a dc voltage, and (iii) experimental access to studies over a wide frequency range of external perturbations (adiabatic and non-adiabatic regime), and transition from overdamped to underdamped dynamic regimes, enabling studies of inertial effects and transition to chaos.Zapata et al.[18] proposed a 3-junction (3JJ) SQUID ratchet, which consists of a superconducting loop of inductance L, intersected by one Josephson junction in one arm and by two Josephson junctions connected in series in the other arm. For vanishing L a quasi-one dimensional (1D) ratchet potential can be obtained, and rectification of an ac bias current for low-and high-frequency drive of such a rocking ratchet has been predicted. In this paper we investigate a 3JJ SQUID, similar to the one proposed in [18]. We derive the equations of motion and the ratchet potential for our type of device, we present its experimental realization, and we investigate its operation as a rocking ratchet for both adiabatic and * Electronic address: koelle@uni-tuebingen. non-adiabatic drive. We also compare experimental results with numerical simulations for our device and for the originally proposed 3JJ SQUID ratchet.We first discuss the underlying dynamic equations, using the resistively and capacitively shunted junction model [22,23]. To simp...

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Deterministic ratchets: Route to diffusive transport

Cited by 62 publications

References 23 publications

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

High-Efficiency Deterministic Josephson Vortex Ratchet

Three-Junction SQUID Rocking Ratchet

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