Soliton Ratchets From Pointlike Inhomogeneities

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Soliton Ratchets From Point-like Inhomogeneities

• Angel Sánchez
• Grupo Interdisciplinar de Sistemas Complejos
• Universidad Carlos III de Madrid, Spain
• Also associated with
• Instituto de Biocomputación y Física de Sistemas
  Complejos (BIFI), Zaragoza, Spain
• http//gisc.uc3m.es/anxo

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Ratchets nonequilibrium rectifiers

• Molecular motors P. Reimann, Phys. Rep. 361,
  56 (2002), ch. 7
• Quantum devices Reimann, ch. 8
  C. S. Lee et al.,
  Nature 400, 337 (1999)
  G. Carapella G. Costabile, PRL 87,
  77002 (2001)
• F.
  Falo et al., Appl. Phys. A 75, 263 (2002)
  J. E. Villegas
  et al., Science 302, 1188 (2003)
• Granular matter C. Marquet et al., PRL 88,
  168301 (2002) S. J. Moon et al., PRL 91,
  134301 (2003) F.
  Alonso-Marroquín H. J. Herrmann, PRL 92, 54301
  (2004) D. van der Meer et al., PRL 92,
  184301 (2004)
• Many moreReimann H. Linke, ed., Appl. Phys. A
  75 (2002)

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Molecular motors
Kinesin/myosin motility on microtubules
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Particle (rocking) ratchets

• No thermal equilibrium
• No spatial inversion symmetry

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Molecular motors
But molecular motors are not point particles!
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Solitons as extended particles
(unperturbed)
Ansatz for the kink center position
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Solitons as extended particles
Collective coordinates approach A. S. A. R.
Bishop, SIAM Rev. 40, 579 (1998)
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Proposals for Soliton Ratchets

• F. Marchesoni, PRL 77, 2364 (1996)
• Z. Csahók et al., PRE 55, 5179 (1997)
• A. V. Savin et al., PLA 229, 279 (1997)
• G. Costantini et al., PRE 65, 51103 (2002)
• M. Salerno N. R. Quintero, PRE 65, 25602
  (2002)N. R. Quintero et al., PRE in press
  (2005)
• Rocking under correlated noise
• Coupled particles Asymmetry in V(u)

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Proposals for Soliton Ratchets

• S. Flach et al., PRL 88, 184101 (2002)
• M. Salerno Y. Zolotaryuk, PRE 65, 51103 (2002)
• L. Morales-Molina et al., PRL 91, 234102 (2003)
• A. Ustinov et al., PRL 93, 87001 (2004)
• Asymmetrically driven, rocking ratchet
• Homogeneous system (no external potential)
• Role of internal mode

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Experiments (Josephson)
G. Carapella G. Costabile, PRL 87, 77002
(2001)
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Experiments (Josephson)
G. Carapella G. Costabile, PRL 87, 77002
(2001)
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Experiments (Josephson)
F. Falo et al., Appl. Phys. A 75, 263 (2002)
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Experiments (Josephson)
F. Falo et al., Appl. Phys. A 75, 263 (2002)
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Experiments (Josephson)
F. Falo et al., Appl. Phys. A 75, 263 (2002)
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Our proposal
Nonlinear Klein-Gordon System
sine-Gordon Josephson
?4 microtubules
M. V. Sataric et al., PRE 48, 589 (1993)
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Our proposal
Nonlinear Klein-Gordon System
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Collective coordinates
Generalized Travelling Wave Ansatz (GTWA) F.G.
Mertens et al., PRB 56, 2510 (1997)
Ansatz
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Collective coordinates
Generalized Travelling Wave Ansatz (GTWA) F.G.
Mertens et al., PRB 56, 2510 (1997)
Multiply by
, substract and integrate
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Collective coordinates
Generalized Travelling Wave Ansatz (GTWA) F.G.
Mertens et al., PRB 56, 2510 (1997)
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Particle picture
Effective ratchet potential
Take the non-relativistic limit
sG
?4
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Particle picture
Effective ratchet potential
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Results
Numerical simulations Deterministic
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Results
Numerical simulations Deterministic
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Results
Numerical simulations Deterministic
A0.35, A0.45, A0.5
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Results
Numerical simulations Stochastic
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Results
Numerical simulations Stochastic
Jumps between deterministic pinned states
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Collective coordinate approach
Comparison to the deterministic case
Qualitatively correct poor quantitative agreement
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Collective coordinate approach
Comparison to the stochastic case
Qualitatively correct poor quantitative agreement
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Improved collective coordinates
Add width as a second degree of freedom
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Improved collective coordinates
Add width as a second degree of freedom
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Improved collective coordinates
Comparison to the deterministic case
Excellent quantitative agreement
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Improved collective coordinates
Comparison to the stochastic case
Excellent quantitative agreement
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Improved collective coordinates
Comparison to the stochastic case
Excellent quantitative agreement
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Summary and conclusions

• Motivation for soliton ratchets
• Nonlinear Klein-Gordon ratchets
• Analytically predicted
• Experimentally feasible Observed in simulations
• Design extended to other ac forces (in progress)
• Width (internal oscillation) crucial
• Size/clustering dependent rectification
• Length scale competition
• Stochastic phenomena new mobility windows
• Applications new devices / molecular motors

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Thanks!

• Niurka R. Quintero, Sevilla
• Luis Morales-Molina, Bayreuth
• Franz G. Mertens, Bayreuth

• N. R. Quintero A. S., Proceedings FisEs 97
  (J. A. Cuesta A. S., eds., Madrid, 1997)
• L. Morales-Molina et al., EPJB 37, 79 (2004)
• L. Morales-Molina et al., PRE, in press (2005)