Annales de l'Institut Fourier
We construct pairs of compact Kähler-Einstein manifolds (Mi,gi,ωi)(i=1,2) of complex dimension n with the following properties: The canonical line bundle Li=⋀nT∗Mi has Chern class [ωi/2π], and for each positive integer k the tensor powers L⊗k1 and L⊗k2 are isospectral for the bundle Laplacian associated with the canonical connection, while M1 and M2 – and hence T∗M1 and T∗M2 – are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but not classically equivalent. Moreover, we construct many examples of line bundles L, pairs of potentials Q1, Q2 on the base manifold, and pairs of connections ∇1, ∇2 on L such that for each positive integer k the associated Schrödinger operators on L⊗k are isospectral.
Gordon, Carolyn; Kirwin, William; Schueth, Dorothee; and Webb, David, "Quantum Equivalent Magnetic Fields that are not Classically Equivalent" (2010). Open Dartmouth: Faculty Open Access Articles. 3140.