English

Quantum tunneling in deep potential wells and strong magnetic field revisited

Mathematical Physics 2023-09-06 v5 math.MP Spectral Theory

Abstract

Inspired by a recent paper^* by C. Fefferman, J. Shapiro and M. Weinstein, we investigate quantum tunneling for a Hamiltonian with a symmetric double well and a uniform magnetic field. In the simultaneous limit of strong magnetic field and deep potential wells with disjoint supports, tunneling occurs and we derive accurate estimates of its magnitude. ^*\,[Lower bound on quantum tunneling for strong magnetic fields. SIAM J. Math. Anal. 54(1), 1105-1130 (2022).]

Keywords

Cite

@article{arxiv.2208.13030,
  title  = {Quantum tunneling in deep potential wells and strong magnetic field revisited},
  author = {B. Helffer and A. Kachmar},
  journal= {arXiv preprint arXiv:2208.13030},
  year   = {2023}
}

Comments

41 pages; corrected and elaborated the proof of Proposition 6.5