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Lower Bounds on Quantum Tunneling for Excited States
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We revisit the problem of quantum tunneling for a particle moving in the continuum, and in the absence of a magnetic field. In all spatial dimensions, we extend previous results to the case where the single-well potential satisfies reflection-symmetry.
Forward citations
Cited by 2 Pith papers
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Magnetic Double-Wells: Lower Bounds on Tunneling
For generic coupling λ in a strongly magnetic double well, the tunneling splitting and hopping coefficient are bounded below by exp(-λ^{1+ε}) outside a zero-density exceptional set.
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Magnetic Double-Wells: Absence of Tunneling
Placing four exponentially small potential bumps at a tunable height around a radial well makes the magnetic double-well hopping coefficient vanish, so the eigenvalue splitting is exactly zero.
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