Abstract
We consider a system of interacting Brownian particles in 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.
| Original language | English |
|---|---|
| Pages (from-to) | 1201-1227 |
| Number of pages | 27 |
| Journal | Annals of Probability |
| Volume | 32 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2004 Apr |
| Externally published | Yes |
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Keywords
- Crystallization
- Interacting Brownian particles
- Rigidity
- Scaling limit
- Zero temperature limit
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Zero temperature limit for interacting Brownian particles. I. Motion of a single body. / Funaki, Tadahisa.
In: Annals of Probability, Vol. 32, No. 2, 04.2004, p. 1201-1227.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Zero temperature limit for interacting Brownian particles. I. Motion of a single body
AU - Funaki, Tadahisa
PY - 2004/4
Y1 - 2004/4
N2 - We consider a system of interacting Brownian particles in 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.
AB - We consider a system of interacting Brownian particles in 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.
KW - Crystallization
KW - Interacting Brownian particles
KW - Rigidity
KW - Scaling limit
KW - Zero temperature limit
UR - http://www.scopus.com/inward/record.url?scp=3042587558&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=3042587558&partnerID=8YFLogxK
U2 - 10.1214/009117904000000180
DO - 10.1214/009117904000000180
M3 - Article
AN - SCOPUS:3042587558
VL - 32
SP - 1201
EP - 1227
JO - Annals of Probability
JF - Annals of Probability
SN - 0091-1798
IS - 2
ER -