Exact saddles and finite-T Picard-Lefschetz contour integrals over quasi-zero modes encode the full resurgent structure and yield non-perturbative splittings for every energy level in the double well.
Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Picard--Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem.
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UNVERDICTED 4representative citing papers
Exact Airy-function evaluation of the Gauss-Bonnet mini-superspace path integral plus Picard-Lefschetz resolution of lapse degeneracies via complex (G ħ) deformation that alters the KSW condition.
Presents explicit trans-series calculations for the double-well spectrum via exact WKB and path integral approaches up to four-instanton level.
CP conservation in QCD follows from taking the infinite volume limit prior to summing over topological sectors, shown consistent with steepest-descent contours and chiral EFT.
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CP conservation in the strong interactions
CP conservation in QCD follows from taking the infinite volume limit prior to summing over topological sectors, shown consistent with steepest-descent contours and chiral EFT.