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arXiv 1505.08087cond-mat.softcond-mat.stat-mech
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一维多运动系统的涌现集体性质

Emergent collective properties of many-motor systems in one dimension

Anton Souslov, Paul M. Goldbart

摘要:

沿着微管,某些主动马达在一个方向上推动自己,而另一些则在相反的方向上推动自己。例如,运输货物的马达蛋白动力蛋白和驱动蛋白分别将它们自身推向微管的所谓正端和负端,并且在这样做时能够彼此通过,但不是没有相互作用。我们讨论了由许多马达组成的系统的涌现集体行为,一些马达向正端推进,另一些马达向负端推进。为了做到这一点,我们在这个强相互作用、远离平衡的经典随机多电机系统和在虚时间中演化的量子力学多体系统之间进行了类比。我们应用量子多体理论,包括自洽的平均场论和玻色化的著名方法,揭示的现象所表现出的多电机系统,如结构的形成和集体模式在低频和长波长的动力学。特别是,通过玻色化的描述,我们发现类似物的手性Luttinger液体,以及一个定性的过渡性质的低频模式-从传播到纯粹的耗散-控制的密度和相互作用强度。

英文摘要:

Along a microtubule, certain active motors propel themselves in one direction whereas others propel themselves in the opposite direction. For example, the cargo transporting motor proteins dynein and kinesin propel themselves towards the so-called plus- and minus-ends of the microtubule, respectively, and in so doing are able to pass one another, but not without interacting. We address the emergent collective behavior of systems composed of many motors, some propelling towards the plus-end and others propelling towards the minus-end. To do this, we used an analogy between this strongly interacting, far-from-equilibrium, classical stochastic many-motor system and a certain quantum-mechanical many-body system evolving in imaginary time. We apply well-known methods from quantum many-body theory, including self-consistent mean-field theory and bosonization, to shed light on phenomena exhibited by the many-motor system such as structure formation and the dynamics of collective modes at low-frequencies and long-wavelengths. In particular, via the bosonized description we find analogs of chiral Luttinger liquids, as well as a qualitative transition in the nature of the low-frequency modes---from propagating to purely dissipative---controlled by density and interaction strength.

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