Investigation reveals quasi intrinsic ultracontractivity of magnetic Schrödinger semigroups, highlighting implications on ground state.
A possible intrinsic ultracontractivity of the magnetic Schrödinger semigroups was investigated. Usually, Rosen inequalities are essential for intrinsic ultracontractivity but hard to find since a specific asymptotical behaviour of the ground state is required. However, in the magnetic case operators of the Schrödinger semigroup are no longer positivity improving. This causes a variety of problems including the use of Logarithmic Sobolev inequalities. Using diamagnetic inequalities quasi intrinsic ultracontractivity was shown in the magnetic case.
No takes yet. Share an insight, caveat, or question.
Christoph Schwerdt (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: