19 citations · 26 across the 8 of their papers we have counts for
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Magnetic Double-Wells: Lower Bounds on Tunneling
Charles L. Fefferman, Jacob Shapiro, Michael I. Weinstein
We study double-well systems with strong magnetic fields and deep potential wells. We present lower bounds on tunneling rates for generic values of the coupling constant. This resu…
Magnetic Double-Wells: Absence of Tunneling
Charles L. Fefferman, Jacob Shapiro, Michael I. Weinstein
We present a magnetic double-well Hamiltonian where the tunneling between the two wells vanishes, as recently announced.
Lower Bounds on Quantum Tunneling for Excited States
Charles L. Fefferman, Jacob Shapiro, Michael I. Weinstein
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…
Quantum tunneling and its absence in deep wells and strong magnetic fields
Charles L. Fefferman, Jacob Shapiro, Michael I. Weinstein
We present new results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field. We construct a family of double well potentials conta…
Discrete honeycombs, rational edges and edge states
C. L. Fefferman, S. Fliss, M. I. Weinstein
Consider the tight binding model of graphene, sharply terminated along an edge parallel to a direction of translational symmetry of the underlying period lattice. We clas…
Honeycomb Schroedinger operators in the strong binding regime
C. L. Fefferman, J. P. Lee-Thorp, M. I. Weinstein
In this article, we study the Schrödinger operator for a large class of periodic potentials with the symmetry of a hexagonal tiling of the plane. The potentials we consider are sup…
Bifurcations of edge states -- topologically protected and non-protected -- in continuous 2D honeycomb structures
C. L. Fefferman, J. P. Lee-Thorp, M. I. Weinstein
This paper summarizes and extends the authors' work on the bifurcation of topologically protected edge states in continuous two-dimensional honeycomb structures. We consider a fami…
Edge states in honeycomb structures
Charles L. Fefferman, James P. Lee-Thorp, Michael I. Weinstein
An edge state is a time-harmonic solution of a conservative wave system, e.g. Schroedinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to…