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arXiv · 1810.00342

Trans-series for the ground state density and Generalized Bloch equation

Edward Shuryak·Alexander V Turbiner
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Abstract

Based on Generalized Bloch equation the trans-series 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 semiclassical terms are still defined by the flucton trajectory (its classical action) and quadratic fluctuations (the determinant), respectively, while the the next-to-next-to-leading correction (at large distances) is of non-perturbative nature. It comes from the fact that all flucton plus multi-instanton, instanton-anti-instanton classical trajectories lead to the same classical action behavior at large distances! This correction is proportional to sum of all leading instanton contributions to energy gap.

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Edward Shuryak, Alexander V Turbiner. 2018-09-30. Trans-series for the ground state density and Generalized Bloch equation. https://doi.org/10.1103/physrevd.98.105007

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