We study the distribution of active, noninteracting particles over two bulk states separated by a ratchet potential. By solving the steady-state Smoluchowski equations in a flux-free setting, we show that the ratchet potential affects the distribution of particles over the bulks and thus exerts an influence of infinitely long range. As we show, an external potential that is nonlinear is crucial for having such a long-range influence. We characterize how the difference in bulk densities depends on activity and on the ratchet potential, and we identify power law dependencies on system parameters in several limiting cases. While weakly active systems are often understood in terms of an effective temperature, we present an analytical solution that explicitly shows that this is not possible in the current setting. Instead, we rationalize our results by a simple transition state model that presumes particles to cross the potential barrier by Arrhenius rates modified for activity. While this model does not quantitatively describe the difference in bulk densities for feasible parameter values, it does reproduce—in its regime of applicability—the complete power law behavior correctly.
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7 November 2018
Research Article|
November 05 2018
Ratchet-induced variations in bulk states of an active ideal gas
Jeroen Rodenburg
;
Jeroen Rodenburg
a)
1
Institute for Theoretical Physics, Utrecht University
, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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Siddharth Paliwal
;
Siddharth Paliwal
2
Soft Condensed Matter Group, Debye Institute for Nanomaterials Science, Utrecht University
, Princetonplein 1, 3584 CC Utrecht, The Netherlands
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Marjolein de Jager;
Marjolein de Jager
1
Institute for Theoretical Physics, Utrecht University
, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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Peter G. Bolhuis
;
Peter G. Bolhuis
3
Van ’t Hoff Institute for Molecular Sciences, University of Amsterdam
, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
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Marjolein Dijkstra
;
Marjolein Dijkstra
2
Soft Condensed Matter Group, Debye Institute for Nanomaterials Science, Utrecht University
, Princetonplein 1, 3584 CC Utrecht, The Netherlands
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René van Roij
René van Roij
b)
1
Institute for Theoretical Physics, Utrecht University
, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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a)
Electronic mail: a.j.rodenburg@uu.nl
b)
Electronic mail: r.vanroij@uu.nl
J. Chem. Phys. 149, 174910 (2018)
Article history
Received:
July 17 2018
Accepted:
October 15 2018
Citation
Jeroen Rodenburg, Siddharth Paliwal, Marjolein de Jager, Peter G. Bolhuis, Marjolein Dijkstra, René van Roij; Ratchet-induced variations in bulk states of an active ideal gas. J. Chem. Phys. 7 November 2018; 149 (17): 174910. https://doi.org/10.1063/1.5048698
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