2017
DOI: 10.1209/0295-5075/119/50007
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A minimal model of an autonomous thermal motor

Abstract: We consider a model of a Brownian motor composed of two coupled overdamped degrees of freedom moving in periodic potentials and driven by two heat reservoirs. This model exhibits a spontaneous breaking of symmetry and gives rise to directed transport in the case of a nonvanishing interparticle interaction strength. For strong coupling between the particles we derive an expression for the propagation velocity valid for arbitrary periodic potentials. In the limit of strong coupling the model is equivalent to the… Show more

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Cited by 43 publications
(50 citation statements)
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“…Most importantly, we notice that the second order term of the velocity vanishes for a phase shift between the potentials ϕ = lπ with l an integer number. This is consistent with the results for the classical counterpart of the present model found in [18], where it was numerically shown that the velocity vanishes for ϕ = lπ independently of the order of V 0 . In this case the system does not break the spatial symmetry discussed in section I.…”
Section: B Second Ordersupporting
confidence: 93%
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“…Most importantly, we notice that the second order term of the velocity vanishes for a phase shift between the potentials ϕ = lπ with l an integer number. This is consistent with the results for the classical counterpart of the present model found in [18], where it was numerically shown that the velocity vanishes for ϕ = lπ independently of the order of V 0 . In this case the system does not break the spatial symmetry discussed in section I.…”
Section: B Second Ordersupporting
confidence: 93%
“…In this section we introduce the autonomous motor model as the quantum conterpart of the classical model introduced in [18]. The system Hamiltonian reads…”
Section: The Modelmentioning
confidence: 99%
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“…Following the terminology of [50], one may say that the classical dynamics is hence only 'weakly' symmetric under global rotations. Now, it can be shown numerically [74] that there is no current in the system whenever f=k π/3 (k is an arbitrary integer), and the current is non-zero whenever k 3 f p ¹ (see figure E1). At the same time, we notice that, whenever f=kπ/3, U j,i =U i, j+k .…”
Section: Appendix B Continuous Limitmentioning
confidence: 99%
“…This is a well-known aspect for stochastic dynamics of coupled components, each evolving at its own temperature (see, e.g. [26][27][28][29][30][31][32][33]). However, in the case at hand this nonzero current has a peculiar form due to the fact that the coupling term in equation (1) is a periodic function of the phase difference.…”
Section: Out-of-equilibrium Currentmentioning
confidence: 99%