176 citations · 768 across the 86 of their papers we have counts for
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Existence and stability of Schrödinger solitons on noncompact manifolds
David Borthwick, Roland Donninger, Enno Lenzmann +1
We consider the focusing nonlinear Schrödinger equation on a large class of rotationally symmetric, noncompact manifolds. We prove the existence of a solitary wave by perturbing of…
Limiting Behaviors of High Dimensional Stochastic Spin Ensembles
Yuan Gao, Kay Kirkpatrick, Jeremy Marzuola +2
Lattice spin models in statistical physics are used to understand magnetism. Their Hamiltonians are a discrete form of a version of a Dirichlet energy, signifying a relationship to…
Nodal deficiency, spectral flow, and the Dirichlet-to-Neumann map
Gregory Berkolaiko, Graham Cox, Jeremy L. Marzuola
It was recently shown that the nodal deficiency of an eigenfunction is encoded in the spectrum of the Dirichlet-to-Neumann operators for the eigenfunction's positive and negative n…
Spectral band degeneracies of rotationally invariant periodic Schrödinger operators
Rachael T. Keller, Jeremy L. Marzuola, Braxton Osting +1
The dynamics of waves in periodic media is determined by the band structure of the underlying periodic Hamiltonian. Symmetries of the Hamiltonian can give rise to novel properties…