Related papers: Interfaces in spectral asymptotics and nodal sets

This article is concerned with asymptotics of equivariant Bergman kernels and partial Bergman kernels for polarized projective Kahler manifolds invariant under a Hamiltonian holomorphic $S^1$ action. Asymptotics of partial Bergman kernel…

The article examines a boundary-value problem in a domain consisting of perforated and imperforate regions, with Neumann conditions prescribed at the boundaries of the perforations. Assuming the porous medium has symmetric, periodic…

We consider the Schroedinger operator with a complex delta interaction supported by two parallel hypersurfaces in the Euclidean space of any dimension. We analyse spectral properties of the system in the limit when the distance between the…

We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive $\delta'$ interaction supported by a smooth surface in $\R^3$, either infinite and asymptotically planar, or compact and closed. Its second term is…

We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schr\"odinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value $b_0$ of the intensity of the magnetic field is strictly…

This study is devoted to the asymptotic spectral analysis of multiscale Schr\"odinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal…

The results of this paper are twofold: In the first part, we prove that for Schr\"odinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic maps which are holomorphic or…

In this paper we study the asymptotic behaviour of the spectral function corresponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. This implies a full asymptotic expansion…

Using Hitchin's parameterization of the Hitchin-Teichm\"uller component of the $SL(n,\mathbb{R})$ representation variety, we study the asymptotics of certain families of representations. In fact, for certain Higgs bundles in the…

We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…

We perform quantitative spectral analysis of the self-adjoint Dirichlet Laplacian $\mathsf{H}$ on an unbounded, radially symmetric (generalized) parabolic layer $\mathcal{P}\subset\mathbb{R}^3$. It was known before that $\mathsf{H}$ has an…

Gapless quantum phases can become distinct when internal symmetries are enforced, in analogy with gapped symmetry-protected topological (SPT) phases. However, this distinction does not always lead to protected edge modes, raising the…

We prove the existence of spectral gaps of Ornstein-Uhlenbeck operators on loop spaces over a class of Riemannian manifolds which include hyperbolic spaces. This is an alternative proof and an extension of a result in Chen-Li-Wu in J.…

We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…

The asymptotic analysis of Bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention. Such interfaces typically occur when the associated limiting Bergman density function…

We establish semiclassical asymptotics and estimates for the Schwartz kernel $e_h(x,y;\tau)$ of spectral projector for a second order elliptic operator on the manifold with a boundary. While such asymptotics for its restriction to the…

We consider interface modes in block disordered subwavelength resonator chains in one dimension. Based on the capacitance operator formulation, which provides a first-order approximation of the spectral properties of dimer-type block…

Inspired by continuum mechanical contact problems with geological fault networks, we consider elliptic second order differential equations with jump conditions on a sequence of multiscale networks of interfaces with a finite number of…

We consider the spectral behavior and noncommutative geometry of commutators $[P,f]$, where $P$ is an operator of order $0$ with geometric origin and $f$ a multiplication operator by a function. When $f$ is H\"{o}lder continuous, the…

We study the ground state of a system with an interface between $\nu=4$ and $\nu=3$ in the quantum Hall regime. Far from the interface, for a range of interaction strengths, the $\nu=3$ region is fully polarized but $\nu=4$ region is…