Strong phase separation in a model of sedimenting lattices
Strong phase separation in a model of sedimenting lattices
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DOI：
10.1103/physreve.61.1648
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发表时间：
1999-07
期刊：
影响因子：
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通讯作者：
Rangan Lahiri;M. Barma;S. Ramaswamy
中科院分区：
文献类型：
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作者：
Rangan Lahiri;M. Barma;S. Ramaswamy
我们研究了在耗散介质中驱动的晶体的不稳定性所导致的稳态，例如，在粘性流体中稳定沉积的胶体晶体。这个问题涉及两个耦合场，密度场和倾斜度场；后者描述了质量张量相对于驱动场的方向。我们将该问题映射到一个一维晶格模型，该模型具有两种耦合的自旋，它们通过守恒动力学演化。在该模型的稳态下，两种物质均表现出宏观的相分离。这种相分离在所有温度或噪声水平下都很稳定，因此被称为强相分离。这种相分离可以理解为再混合的障碍，它随着系统规模的增长而增长，并导致对数缓慢地接近稳态。在特定的对称极限下，即使初始模型只有局部动力学，对于具有无限范围相互作用的哈密顿量，详细平衡的条件仍然成立。相互作用的长程特性是相分离的原因，也是它在所有温度下都持续存在的原因。讨论了可能的实验方法。
We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a one-dimensional lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels- hence the term strong phase separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.