耦合双粒子在不对称体系中的输运现象研究

发布时间：2019-01-20 11:17

【摘要】：输运现象广泛存在于自然界之中,对这些现象的研究具有重要的理论与现实意义。作为一种独特的类型,周期性不对称体系中产生输运现象并不要求净外力或者相应物理量梯度的存在,空间对称性的破缺结合具有一定自相关时间的无偏外扰动即足以使体系中产生定向输运,这类现象被称为棘轮效应,或者布朗马达。通常宏观情况下粒子被当作单质点模型处理,因而忽略了粒子本身的结构对运动的影响。然而有些时候这样的忽略是不适宜的,尤其是当粒子本身的尺寸与体系的空间结构可相比拟时,此时粒子的内部相互作用以及本身结构的不对称性等因素都会对体系的输运性质产生很大的影响,甚至可以造成输运方向的反转变化。为了研究内部相互作用对体系输运性质的影响,我们考虑了两个弹性耦合在一起的相同粒子,它们被置于同一个热环境与不对称锯齿势之下,并且都受到了外加随机色扰动的作用。我们重点研究耦合双粒子体系的输运性质与弹性耦合作用之间的关系,发现体系的流对耦合参数具有依赖性,尤其是当粒子间平衡距离的长度位于锯齿势的两个坡长之间时,流向可以在特定的弹性系数值处产生反转。为了解释这样的流向反转现象,我们对比了无耦合与刚性耦合两种极限情况。在无耦合情况下,两个粒子在原始锯齿势中独立运动;而在刚性耦合情况下,两个粒子可以看作一个在等效势下运动的等效单粒子。通过对照等效势与原始势,我们发现当粒子间平衡距离位于原始势两个坡长之间时,等效势的不对性相对于原始势会产生反转,而势的不对称反转则会导致流向的反转。在宏观尺度下,热噪声一般被当作高斯白噪声处理,然而很多研究显示分子尺度下热噪声的时间关联性已不可忽略,因此已不适合继续将其处理为白噪声形式。由于分子本身的结构特点,它也不适合被处理为单质点模型,分子的指向也会对其运动行为产生影响。为了研究分子尺度热噪声以及分子结构的不对称性对体系输运性质的影响,我们考虑了一个简单的不对称模型分子,它由两个不同的部分刚性组合而成,并维持它的指向。我们将分子沿不同方向运动的不同表现为阻尼的不同,然后选取合适的模型以模拟热噪声,通过计算发现不对称分子可以朝阻尼较小的方向产生定向运动,这说明分子本身结构所提供的不对称性结合热噪声的时间关联性可以使得分子产生定向运动。然而如果分子的指向不被维持,那么这种定向运动则会很快消失,因此这种现象并不违反热力学第二定律。
[Abstract]:Transport phenomena exist widely in nature, and the study of these phenomena has important theoretical and practical significance. As a unique type, transport in periodic asymmetric systems does not require the existence of net external forces or the corresponding physical gradient. The breaking and breaking of space symmetry and the unbiased external disturbance with a certain autocorrelation time are sufficient to produce directional transport in the system. This phenomenon is called ratchet effect or Brownian motor. In general, the particle is treated as a single mass point model under macroscopic conditions, thus neglecting the effect of the structure of the particle itself on the motion. Sometimes, however, such neglect is inappropriate, especially when the size of the particle itself is comparable to the spatial structure of the system. At this time, the internal interaction of particles and the asymmetry of their own structure will have a great impact on the transport properties of the system, and even lead to the reversal of the transport direction. In order to study the effect of internal interaction on the transport properties of the system, we consider two identical particles that are elastically coupled together, which are placed under the same thermal environment and asymmetric sawtooth potential. All of them are affected by random color perturbation. We focus on the relationship between the transport properties of the coupled two-particle system and the elastic coupling. It is found that the flow of the system is dependent on the coupling parameters, especially when the length of the equilibrium distance between particles lies between the two sloping lengths of the sawtooth potential. The flow direction can be reversed at a particular value of elasticity. In order to explain the flow reversal phenomenon, we compare the two limit cases of uncoupled and rigid coupling. In the case of no coupling, two particles move independently in the original sawtooth potential, while in the case of rigid coupling, the two particles can be regarded as an equivalent single particle moving under the equivalent potential. By comparing the equivalence potential with the original potential, we find that when the equilibrium distance between the particles lies between the two slope lengths of the original potential, the asymmetry reversal of the equivalent potential will lead to the reversal of the flow direction. At macro scale, thermal noise is generally treated as Gao Si white noise. However, many studies show that the temporal correlation of thermal noise at molecular scale can not be ignored, so it is not suitable to continue to treat thermal noise as white noise. Because of the structural characteristics of the molecule itself, it is not suitable to be treated as a single particle model, and the direction of the molecule will have an effect on its motion behavior. In order to study the effect of molecular scale thermal noise and the asymmetry of molecular structure on the transport properties of the system, we consider a simple asymmetric model molecule, which is composed of two different partial rigidities, and maintains its direction. In this paper, we show that the molecules moving in different directions are different in damping, and then we select the appropriate model to simulate the thermal noise, and we find that the asymmetrical molecules can produce directional motion in the direction of less damping. It is suggested that the time correlation of asymmetric and thermal noise can lead to directional motion of the molecule. However, if the direction of the molecule is not maintained, the directional motion will soon disappear, so this phenomenon does not violate the second law of thermodynamics.
【学位授予单位】：中国科学院研究生院(上海应用物理研究所)
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O572.2

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