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Zero temperature limit for interacting Brownian particles. I: Motion of a single body. (English) Zbl 1121.82028

Summary: We consider a system of interacting Brownian particles in \(\mathbb R^d\) with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes \(a>0\). The asymptotic behavior of the system is studied under the zero temperature limit from both microscopic and macroscopic aspects. If the system is rigidly crystallized, namely if the particles are rigidly arranged in an equal distance a, the crystallization is kept under the evolution in macroscopic time scale. Then, assuming that the crystal has a definite limit shape under a macroscopic spatial scaling, the translational and rotational motions of such shape are characterized.
Part II, cf. Ann. Probab. 32, No. 2, 1228–1246 (2004; Zbl 1122.82029).

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory

Citations:

Zbl 1122.82029
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References:

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