Results 11 to 20 of about 568 (47)

Semiclassical limits of eigenfunctions on flat $n$-dimensional tori [PDF]

, 2011
We provide a proof of the conjecture formulated in \cite{Jak97,JNT01} which states that on a $n$-dimensional flat torus $\T^{n}$, the Fourier transform of squares of the eigenfunctions $|\phi_\lambda|^2$ of the Laplacian have uniform $l^n$ bounds that do
Bourgain, Connes, Hörmander, Levitan,, Mockenhaupt, Sogge, Sogge, Tayeb Aϊssiou, Toth   +8 more
core   +1 more source

On the behavior of clamped plates under large compression [PDF]

, 2019
We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions.
Antunes, Pedro R. S., Buoso, D., Freitas, P.   +2 more
core   +1 more source

On the asymptotic number of low-lying states in the two-dimensional confined Stark effect

Forum of Mathematics, Sigma
We investigate the Stark operator restricted to a bounded domain $\Omega \subset \mathbb {R}^2$ with Dirichlet boundary conditions. In the semiclassical limit, a three-term asymptotic expansion for its individual eigenvalues has been established ...
Larry Read
doaj   +1 more source

The Fate of the Landau Levels under Perturbations of Constant Sign

, 2009
We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schr\"odinger operator with constant magnetic field, by bounded electric potentials of fixed sign.
Klopp, Frédéric, Raikov, Georgi
core   +3 more sources

On the lower bound of the inner radius of nodal domains

, 2019
We discuss the asymptotic lower bound on the inner radius of nodal domains that arise from Laplacian eigenfunctions \varphi _{\lambda} on a closed Riemannian manifold (M, g) .
Georgiev, B.
core   +1 more source

Spectral Shift Function for the Perturbations of Schrödinger Operators at High Energy [PDF]

, 2008
2000 Mathematics Subject Classification: 35P20, 35J10, 35Q40.We give a complete pointwise asymptotic expansion for the Spectral Shift Function for Schrödinger operators that are perturbations of the Laplacian on Rn with slowly decaying ...
Assel, Rachid, Dimassi, Mouez
core  

Around multivariate Schmidt-Spitzer theorem

, 2013
Given an arbitrary complex-valued infinite matrix A and a positive integer n we introduce a naturally associated polynomial basis B_A of C[x0...xn]. We discuss some properties of the locus of common zeros of all polynomials in B_A having a given degree m;
Alexandersson, Per, Shapiro, Boris
core   +1 more source

Accuracy on eigenvalues for a Schrodinger operator with a degenerate potential in the semi-classical limit [PDF]

, 2006
We consider a semi-classical Schrodinger operator with a degenerate potential V(x,y) =f(x) g(y) . g is assumed to be a homogeneous positive function of m variables and f is a strictly positive function of n variables, with a strict minimum. We give sharp
Morame, Abderemane, Truc, Francoise
core   +2 more sources

Eigenvalue asymptotic of Robin Laplace operators on two-dimensional domains with cusps

, 2010
We consider Robin Laplace operators on a class of two-dimensional domains with cusps. Our main results include the formula for the asymptotic distribution of the eigenvalues of such operators.
Kovarik, Hynek
core   +1 more source

Quantum resonances and partial differential equations

, 2002
Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state.
Zworski, Maciej
core   +2 more sources