The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and Positive Friction

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• 作者：David P. Herzog ; Scott Hottovy ; Giovanni Volpe
• 关键词：Small ; mass limit ; Smoluchowski–Kramers approximation ; Locally Lipschitz coefficients
• 刊名：Journal of Statistical Physics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：163
• 期：3
• 页码：659-673
• 全文大小：480 KB
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• 作者单位：David P. Herzog (1)
  Scott Hottovy (2)
  Giovanni Volpe (3) (4)
  
  1. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA
  2. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53706, USA
  3. Soft Matter Lab, Department of Physics, Bilkent University, 06800, Ankara, Turkey
  4. UNAM-Institute of Material Science and Nanotechnology, Bilkent University, 06800, Ankara, Turkey
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

A class of Langevin stochastic differential equations is shown to converge in the small-mass limit under very weak assumptions on the coefficients defining the equation. The convergence result is applied to three physically realizable examples where the coefficients defining the Langevin equation for these examples grow unboundedly either at a boundary, such as a wall, and/or at the point at infinity. This unboundedness violates the assumptions of previous limit theorems in the literature. The main result of this paper proves convergence for such examples.