Search results for "Eigenfunction"
showing 10 items of 58 documents
Methods for Calculating Bending Moment and Shear Force in the Moving Mass Problem
2004
Two methods able to capture with different levels of accuracy the discontinuities in the bending moment and shear force laws in the dynamic analysis of continuous structures subject to a moving system modeled as a series of unsprung masses are presented. The two methods are based on the dynamic-correction method, which improves the conventional series expansion by means of a pseudostatic term, and on an eigenfunction series expansion of the continuous system response, which takes into account the effect of the moving masses on the structure, respectively.
Supersymmetric associated vector coherent states and generalized Landau levels arising from two-dimensional supersymmetry
2008
We describe a method for constructing vector coherent states for quantum supersymmetric partner Hamiltonians. The method is then applied to such partner Hamiltonians arising from a generalization of the fractional quantum Hall effect. Explicit examples are worked out.
Waveguides. Radiation Principle. Scattering Matrices
2021
Chapter 2 exposes a mathematical model of a waveguide with several cylindrical ends going to infinity, basic notions and mathematical results (with complete proofs) needed in successive chapters: waves, continuous spectrum eigenfunctions, intrinsic radiation principle, and scattering matrices.
Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field
1992
In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.
Preparation of coherent superposition in a three-state system by adiabatic passage
2004
We examine the topology of eigenenergy surfaces associated to a three-state system driven by two quasi-resonant fields. We deduce mechanisms that allow us to generate various coherent superposition of two states using an additional field, far off resonances. We report the numerical validations in mercury atoms as a model system, creating the coherent superpositions of two excited states and of two states coupled by a Raman process.
Multidimensional Borg–Levinson theorems for unbounded potentials
2018
We prove that the Dirichlet eigenvalues and Neumann boundary data of the corresponding eigenfunctions of the operator $-\Delta + q$, determine the potential $q$, when $q \in L^{n/2}(\Omega,\mathbb{R})$ and $n \geq 3$. We also consider the case of incomplete spectral data, in the sense that the above spectral data is unknown for some finite number of eigenvalues. In this case we prove that the potential $q$ is uniquely determined for $q \in L^p(\Omega,\mathbb{R})$ with $p=n/2$, for $n\geq4$ and $p>n/2$, for $n=3$.
Nonlinear Eigenvalue Problems of Schrödinger Type Admitting Eigenfunctions with Given Spectral Characteristics
2002
The following work is an extension of our recent paper [10]. We still deal with nonlinear eigenvalue problems of the form in a real Hilbert space ℋ with a semi-bounded self-adjoint operator A0, while for every y from a dense subspace X of ℋ, B(y ) is a symmetric operator. The left-hand side is assumed to be related to a certain auxiliary functional ψ, and the associated linear problems are supposed to have non-empty discrete spectrum (y ∈ X). We reformulate and generalize the topological method presented by the authors in [10] to construct solutions of (∗) on a sphere SR ≔ {y ∈ X | ∥y∥ℋ = R} whose ψ-value is the n-th Ljusternik-Schnirelman level of ψ| and whose corresponding eigenvalue is t…
Königs eigenfunction for composition operators on Bloch and H∞ type spaces
2017
Abstract We discuss when the Konigs eigenfunction associated with a non-automorphic selfmap of the complex unit disc that fixes the origin belongs to Banach spaces of holomorphic functions of Bloch and H ∞ type. In the latter case, our characterization answers a question of P. Bourdon. Some spectral properties of composition operators on H ∞ for unbounded Konigs eigenfunction are obtained.
Lévy flights in an infinite potential well as a hypersingular Fredholm problem.
2016
We study L\'evy flights {{with arbitrary index $0< \mu \leq 2$}} inside a potential well of infinite depth. Such problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schr\"odinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain $D$, reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numer…
Quantum counter-propagation in open optical cavities via the quasi-normal-mode approach
2006
By using the quasi-normal-mode (QNM) formalism in a second quantization scheme, the problem of the counter-propagation of electromagnetic fields inside optical cavities is studied. The links between QNM operators and canonical destruction and creation operators describing the external free field, as well as the field correlation functions, are found and discussed. An application of the theory is performed for open cavities whose refractive index satisfies symmetric properties.