2018/09/30 by Edward Shuryak, Alexander V. Turbiner, Alexander V Turbiner · 10 citations
Mathematics · Physics and Astronomy · #Action (physics) #Cold Atom Physics and Bose-Einstein Condensates #Double-well potential #Geometry #Ground state #Instanton #Mathematical physics #Mathematics #Physics #Quadratic equation #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum electrodynamics #Quantum mechanics #Quantum tunnelling #Semiclassical physics #Spectroscopy and Quantum Chemical Studies #Trajectory #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevd.98.105007
published in Physical review. D/Physical review. D. 98(10) (American Physical Society) · 21 pages, 1 figure
arxiv created 2018/09/30 · openalex created_date 2018/10/05 · openalex publication_date 2018/11/16 · arxiv updated 2018/11/21 · openalex updated_date 2026/08/05
Based on the generalized Bloch equation, the transseries expansion for the phase (exponent) of the ground state density for double-well potential is constructed. It is shown that the leading and next-to-leading terms in semiclassical expansion are still defined by the flucton trajectory (its classical action) and quadratic fluctuations (the determinant), respectively, while the next-to-next-to-leading term (at large distances) is of nonperturbative nature. It comes from the fact that all flucton classical trajectories modified by multi-instanton, instanton--anti-instanton additions lead to the same classical action behavior at large distances. This correction is proportional to sum of all leading instanton contributions to energy gap.