Testing the energy diffusion approximation for the escape of a Brownian particle from a potential pocket |
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| Institution: | 1. Physics and Chemistry Department, Omsk State Transport University, Omsk 644046, Russia;2. Physics Department, Omsk State Technical University, Omsk 644050, Russia;1. Univ. Lille, IMT Lille Douai, Univ. Artois, Yncrea Hauts-de-France, ULR 4515 - LGCgE, Laboratoire de Génie Civil et géo-Environnement, F-59000 Lille, France;2. Département de Génie Physique, (LPMF).Université des Sciences et de la Technologie d''Oran, Mohamed Boudiaf. Oran, Algeria;1. Department of Information Engineering, Electrical Engineering and Applied Mathematics (DIEM), University of Salerno, Via Giovanni Paolo II, 132, I-84084 Fisciano, Italy;2. Department of Engineering, University of Sannio, Corso Garibaldi, 107, I-82100 Benevento, Italy;3. Department of Sciences and Technologies and CNISM unit Salerno, University of Sannio, Via Port’Arsa, 11, I-82100 Benevento, Italy;1. Department of Mathematics, Shanghai University, Shanghai, 200444, Shanghai, People’s Republic of China;2. National University of Computer and Emerging Sciences, Lahore Campus, Pakistan;3. National University of Computer and Emerging Sciences, Chiniot-Faisalabad Campus, Pakistan;4. School of Mathematical Sciences, Jiangsu Key Labortary for NSLSCS, Nanjing Normal University, Nanjing, 210023, People’s Republic of China;1. Department of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, China;2. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON M5S 3G8, Canada;3. Baotou Vocational & Technical College, Baotou, 014030, China |
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| Abstract: | For the first time, the energy diffusion approximation is confronted at the percent level with the exact numerical modeling of thermal decay of a metastable state. This model is useful in many branches of natural sciences: e.g. in biology, nuclear physics, chemistry, etc. The exact (within the statistical errors about 2%) quasistationary decay rates result from the Langevin equations for the coordinate and conjugated momentum. For the energy (or action) diffusion approach, a Langevin-type equation for the action is constructed, validated, and solved numerically. The comparison of these two approaches is performed for four potentials (two of which are anharmonic) in a wide range of two dimensionless scaling parameters: i) the governing parameter G reflecting how high is the barrier with respect to the temperature and ii) the damping parameter φ expressing the friction strength. It turns out that the energy diffusion approach produces the rate which comes into 50%-agreement with the exact one only at φ < 0.02. Thus, we quantify, for the first time by our knowledge, the condition φ ≪ 1 known in the literature. |
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