Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bions and Instantons in Triple-well and Multi-well Potentials   Quantum systems with multiple degenerate classical harmonic minima exhibit
new non-perturbative phenomena which are not present for the double-well and
periodic potentials. The simplest characteristic example of this family is the
triple-well potential. Despite the fact that instantons are exact semiclassical
solutions with finite and minimal action, they do not contribute to the energy
spectrum at leading order in the semiclassical analysis. This is because the
instanton fluctuation prefactor vanishes, which can be interpreted as the
action becoming infinite quantum mechanically. Instead, the non-perturbative
physics is governed by different types of {\it bion} configurations. A
generalization to supersymmetric and quasi-exactly soluble models is also
discussed. An interesting pattern of interference between topological and
neutral bions, depending on the hidden topological angle, the discrete theta
angle and the perturbative level number, leads to an intricate pattern of
divergent/convergent expansions for low lying states, and provides criteria for
the exact solvability of some of the states. We confirm these semiclassical
bion predictions using the Bender-Wu Mathematica package to study the structure
of the associated perturbative expansions. It also turns out that all the
systems we study have a curious exact one-to-one relationship between the
perturbative coefficients of the three wells, which we check using the BenderWu
package.

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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: ao-sci