Lower Bounds on Quantum Tunneling for Excited States

Charles L. Fefferman; Jacob Shapiro; Michael I. Weinstein

doi:10.1007/s12220-025-02196-w

Lower Bounds on Quantum Tunneling for Excited States

Charles L. Fefferman
, Jacob Shapiro
, Michael I. Weinstein

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	357
Journal	Journal of Geometric Analysis
Volume	35
Issue number	11
DOIs	https://doi.org/10.1007/s12220-025-02196-w
State	Published - Nov 2025

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Functional analysis
PDEs
Quantum tunneling
Semiclassical

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10.1007/s12220-025-02196-w

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title = "Lower Bounds on Quantum Tunneling for Excited States",

abstract = "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.",

keywords = "Functional analysis, PDEs, Quantum tunneling, Semiclassical",

author = "Fefferman, \{Charles L.\} and Jacob Shapiro and Weinstein, \{Michael I.\}",

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doi = "10.1007/s12220-025-02196-w",

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AU - Fefferman, Charles L.

AU - Shapiro, Jacob

AU - Weinstein, Michael I.

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PY - 2025/11

Y1 - 2025/11

N2 - 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.

AB - 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.

KW - Functional analysis

KW - PDEs

KW - Quantum tunneling

KW - Semiclassical

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UR - https://www.scopus.com/pages/publications/105016360770#tab=citedBy

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DO - 10.1007/s12220-025-02196-w

M3 - Article

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SN - 1050-6926

VL - 35

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

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ER -

Lower Bounds on Quantum Tunneling for Excited States

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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