2007/01/31 by D. G. Levkov, A. G. Panin, Sergey Sibiryakov +1 · 3 citations
Mathematics · Physics and Astronomy · #Chaotic #Classical mechanics #Computer science #Degrees of freedom (physics and chemistry) #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Quantum tunnelling #Scientific Research and Discoveries #Semiclassical physics #Statistical physics #Theoretical and Computational Physics #hep-th #math-ph #math.MP #nlin.CD #physics.chem-ph #quant-ph
paper · pdf · doi:10.1103/physreve.76.046209
published as Phys.Rev.E76:046209,2007 · 21 pages, RevTeX style, 15 figures. Journal version; abstract, introduction and discussion modified, references added
openalex publication_date 2007/10/09 · arxiv created 2007/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop the semiclassical method of complex trajectories in application to chaotic dynamical tunneling. First, we suggest a systematic numerical technique for obtaining complex tunneling trajectories by the gradual deformation of the classical ones. This provides a natural classification of the tunneling solutions. Second, we present a heuristic procedure for sorting out the least suppressed trajectory. As an illustration, we apply our technique to the process of chaotic tunneling in a quantum mechanical model with two degrees of freedom. Our analysis reveals rich dynamics of the system. At the classical level, there exists an infinite set of unstable solutions forming a fractal structure. This structure is inherited by the complex tunneling paths and plays a central role in the semiclassical study. The process we consider exhibits the phenomenon of optimal tunneling: the suppression exponent of the tunneling probability has a local minimum at a certain energy which is thus (locally) the optimal energy for tunneling. We test the proposed method by comparison of the semiclassical results with the results of the exact quantum computations and find a good agreement.