Related papers: Strong diamagnetism for general domains and applic…

In this sequel we extend the derivation of the third order helicity to magnetic fields supported on unlinked domains in 3-space. The formula is expressed in terms of generators of the deRham cohomology of the configuration space of three…

We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. In Part I, we introduced a general formalism for describing such systems and presented the mean…

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and…

We study spectral stability of the $\bar\partial$-Neumann Laplacian on a bounded domain in $\mathbb{C}^n$ when the underlying domain is perturbed. In particular, we establish upper semi-continuity properties for the variational eigenvalues…

In this paper we study the eigenvalue sums of Dirichlet Laplacians on bounded domains. Among our results we establish an improvement of the Li-Yau bound in the presence of a constant magnetic field.

Blazar observations point toward the possible presence of magnetic fields over intergalactic scales of the order of up to $\sim1\,$Mpc, with strengths of at least $\sim10^{-16}\,$G. Understanding the origin of these large-scale magnetic…

We study an eigenvalue problem for the infinity-Laplacian on bounded domains. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction. The work also contains existence results when the parameter, in the…

We prove that for any domain in the Heisenberg group the (k+1)'th Neumann eigenvalue of the sub-Laplacian is strictly less than the k'th Dirichlet eigenvalue. As a byproduct we obtain similar inequalities for the Euclidean Laplacian with a…

The coexistence of the superconductivity and magnetism in the Ho$_{1-x}$Dy$_x$Ni$_2$B$_2$C is studied by using Ginzburg-Landau theory. This alloy shows the coexistence and complex interplay of superconducting and magnetic order. We propose…

We analyze the spectrum of the Laplace operator, subject to homogeneous complex magnetic fields in the plane. For real magnetic fields, it is well-known that the spectrum consists of isolated eigenvalues of infinite multiplicities (Landau…

We consider the Ginzburg-Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. We determine an accurate asymptotic formula for the minimizing energy when the Ginzburg-Landau parameter and…

Simultaneous measurements of position and momentum are considered in $n$ dimensions. We find, that for a particle whose position is strictly localized in a compact domain $D\subset \mathbb{R}^n$ (spatial uncertainty) with non-empty…

We provide the estimates for the constant in the weighted Poincar\'e inequality for a special class of planar domains and weights. Based on this, we prove the lower bounds for the first non-zero eigenvalue $\mu_\rho$ of the Neumann…

We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition ensuring the existence of the discrete spectrum in the strong magnetic field limit.

The sum of the first $n \geq 1$ eigenvalues of the Laplacian is shown to be maximal among triangles for the equilateral triangle, maximal among parallelograms for the square, and maximal among ellipses for the disk, provided the ratio…

It is developed a microscopic description of superconductivity in ferromagnetic materials with triplet pairing triggered by the exchange of magnetic fluctuations. Instead widely used paramagnon model we work with phenomenological spectrum…

It is widely known that the spectrum of the Dirichlet Laplacian is stable under small perturbations of a domain, while in the case of the Neumann or mixed boundary conditions the spectrum may abruptly change. In this work we discuss an…

Motivated by some recent studies of the magnetic Laplacian on Riemannian manifolds, we focus on the first eigenvalue of the magnetic horizontal Laplacian on contact manifolds. We characterize conditions for positive spectral shift, and…

A multi-band effective-mass Hamiltonian is derived for lattice-matched semiconductor nanostructures in a slowly varying external magnetic field. The theory is derived from the first-principles magnetic-field coupling Hamiltonian of Pickard…

We determine constraints on the form of axisymmetric toroidal magnetic fields dictated by hydrostatic balance in a type II superconducting neutron star with a barotropic equation of state. Using Lagrangian perturbation theory, we find the…