arXiv subjects
Publications and source records attributed to Rohan Ghanta.
In 1996 Erdoes showed that among planar domains of fixed area, the smallest principal eigenvalue of the Dirichlet Laplacian with a constant magnetic field is uniquely achieved on the disk. We establish a quantitative version of this inequality, with an explicit remainder term depending on the field strength that measures how much the domain deviates from the disk.
We consider a Fr\"ohlich polaron bound in a symmetric Mexican hat-type potential. The ground state is unique and therefore invariant under rotations. However, we show that the minimizers of the corresponding Pekar problem are nonradial. Assuming these nonradial minimizers are unique up to rotation, we prove in the strong-coupling limit that the ground-state electron density converges in a weak sense to a rotational average of the densities of the minimizers.
The ground-state electron density of a polaron bound to a Coulomb potential in a homogeneous magnetic field--the transverse coordinates integrated out--converges pointwise and weakly in the strong magnetic field limit to the square of a hyperbolic secant function.
We consider the one-dimensional Froehlich polaron localized in a symmetric decreasing electric potential. It is known that the non-linear Pekar functional corresponding to our model admits a unique minimizer. In the strong-coupling limit, we show that any approximate ground-state wave function of our model- after integrating out its phonon modes- converges in the weak sense to this unique minimizer.