clopen.solutions

Open problems

980 registered problems.

OP-00267 Open
Localization at every disorder strength in two dimensions
SP · AIM Open Applied Problems · Anderson localization · random Schrödinger operators
OP-00292 Open
The three-dimensional Lieb–Thirring constant
SP · AIM Open Applied Problems · Lieb–Thirring inequalities · Schrödinger operators · sharp constants
OP-00326 Open
Diffusive mean-square displacement at fixed disorder
MP · AIM Open Applied Problems · Anderson model · quantum diffusion · random Schrödinger operators
OP-00335 Open
Irreducibility of complex Fermi varieties
SP · AIM Open Applied Problems · embedded eigenvalues · Fermi varieties · periodic Schrödinger operators
OP-00347 Open
Full-order resonance growth for every nonzero real compact potential
SP · AIM Open Applied Problems · scattering resonances · Schrödinger operators
OP-00355 Open
Completeness of modes for slowly growing imaginary Schrödinger potentials
SP · AIM Open Applied Problems · completeness of eigenfunctions · non-self-adjoint operators · Schrödinger operators
OP-00359 Open
Nonempty spectrum for a magnetic complex Airy operator at every field strength
SP · AIM Open Applied Problems · magnetic Schrödinger operators · non-self-adjoint operators · superconductivity
OP-00381 Open
Simon’s multidimensional weighted square-integrability conjecture
SP · absolutely continuous spectrum · AIM Open Applied Problems · decaying potentials · Schrödinger operators
OP-00383 Open
Anderson localization for the cosine skew-shift model at every coupling
SP · AIM Open Applied Problems · Anderson localization · discrete Schrödinger operators · skew-shifts
OP-00421 Solution claimed
Does subcritical heat flow always decay faster?
AP · AIM Open Applied Problems · criticality theory · heat kernels · Schrödinger operators
OP-00425 Open
Classical attenuation versus uniform semiclassical local decay
AP · AIM Open Applied Problems · dissipative Schrödinger operators · local decay · semiclassical analysis
OP-00530 Open
Global uniqueness from inverse backscattering data
AP · AIM Open Applied Problems · backscattering data · inverse scattering · Schrödinger operators
OP-00663 Solution claimed
Extended states in the three-dimensional Anderson model
SP · absolutely continuous spectrum · AIM Open Applied Problems · Anderson model · random Schrödinger operators
OP-00732 Solution claimed
Uniform boundedness of the first atomic ionization energy
SP · AIM Open Applied Problems · Coulomb systems · ionization conjecture · many-body Schrödinger operators