2005/09/03 by Tiezheng Qian, Weiqing Ren, Qian, Tiezheng +8
Engineering · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #FOS: Physical sciences #Quantum and electron transport phenomena #Semiconductor Quantum Structures and Devices #Statistical Mechanics (cond-mat.stat-mech) #Superconductivity (cond-mat.supr-con) #cond-mat.stat-mech #cond-mat.supr-con
paper · pdf · doi:10.48550/arxiv.cond-mat/0509076
12 pages including 10 figures
arxiv created 2005/09/03 · openalex publication_date 2005/09/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the string method, originally designed for the study of thermally activated rare events, to the calculation of quantum tunneling rates. This generalization is based on the analogy between quantum mechanics and statistical mechanics in the path-integral formalism. The quantum string method first locates, in the space of imaginary-time trajectories, the minimal action path (MAP) between two minima of the imaginary-time action. From the MAP, the saddle-point (``bounce'') action associated with the exponential barrier penetration probability is obtained and the pre-exponential factor (the ratio of determinants) for the tunneling rate evaluated using stochastic simulation. The quantum string method is implemented to calculate the zero-temperature escape rates for the metastable zero-voltage states in the current-biased Josephson tunnel junction model. In the regime close to the critical bias current, direct comparison of the numerical and analytical results yields good agreement. Our calculations indicate that for the nanojunctions encountered in many experiments today, the (absolute) escape rates should be measurable at bias current much below the critical current.