{getToc} $title={Table of Contents}
Summary
The article discusses the phenomenon of quantum tunneling in deep potential wells and strong magnetic fields, presenting new results on the general case where the single well is not radially symmetric.
Highlights
- Quantum tunneling is a phenomenon of central importance in quantum systems.
- The magnetic case is far more subtle than the non-magnetic case.
- A family of double well potentials is constructed, containing cases for which the low-energy eigenvalue splitting vanishes, and hence quantum tunneling is eliminated.
- The magnetic ground state can be made to transition from symmetric to anti-symmetric by deforming within this family.
- For typical double wells in a certain regime, tunneling is not suppressed, and a lower bound for the eigenvalue splitting is provided.
- The results suggest an approach to achieving flat bands, which are of great interest in the study of strongly-correlated quantum systems.
- The proofs rely on basic estimates on analytic functions and could prove useful for other problems in mathematical physics.
Key Insights
- The article establishes surprising phenomena in magnetic systems, in strong contrast to the long-understood phenomena in non-magnetic systems, highlighting the complexity of quantum tunneling in magnetic fields.
- The construction of quantum double well systems where tunneling is completely eliminated in a strong magnetic field raises questions about the potential for experimental observation of such phenomena.
- The ability to transition the ground state from symmetric to anti-symmetric through deformation of the double well potential suggests a high degree of control over the quantum states.
- The lower bound on the eigenvalue splitting for typical double wells indicates that while tunneling may be suppressed in certain cases, it remains a significant effect in many situations.
- The approach to achieving flat bands through the manipulation of double well potentials could have significant implications for the study of strongly-correlated quantum systems.
- The reliance on basic estimates on analytic functions highlights the importance of mathematical rigor in understanding complex quantum phenomena.
- The article opens up new avenues for research into quantum tunneling and flat bands, with potential applications in quantum computing and materials science.
Mindmap
If MindMap doesn't load, go to the Homepage and visit blog again or Switch to Android App (Under Development).
Citation
Fefferman, C. L., Shapiro, J., & Weinstein, M. I. (2024). Quantum tunneling and its absence in deep wells and strong magnetic fields (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.21100