Search results for "Eigenvalue perturbation"

showing 2 items of 2 documents

Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

2011

We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\dagger]=0$ and $x^\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as $h_1$ and whose eigenvectors are related to those of $h_1$ by $x^\dagger$. Here we extend this procedure to build up a second hamiltonian, whose eigenvalues are different from those of $h_1$, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian hamiltonians.

PhysicsQuantum PhysicsGeneral Physics and AstronomyFOS: Physical sciencesMathematical Physics (math-ph)Eigenvalues and eigenvectors of the second derivativeMathematics::Geometric Topologylaw.inventionGood quantum numbersymbols.namesakeintertwining relationsOperator (computer programming)IsospectralInvertible matrixlawQuantum electrodynamicssymbolsHamiltonian (quantum mechanics)Quantum Physics (quant-ph)Settore MAT/07 - Fisica MatematicaEigenvalues and eigenvectorsEigenvalue perturbationMathematical PhysicsMathematical physics
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Interior Eigenvalue Density of Jordan Matrices with Random Perturbations

2017

International audience; We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E. B. Davies and M. Hager shows that as the dimension of the matrix gets large, with probability close to 1, most of the eigenvalues are close to a circle.We study the expected eigenvalue density of the perturbed Jordan block in the interior of that circle and give a precise asymptotic description.; Nous étudions la distribution de valeurs propres d’un grand bloc de Jordan soumis à une petite perturbation gaussienne aléatoire. Un résultat de E. B. Davies et M. Hager montre que quand la dimension de la matrice devient grande, alors avec probabilité…

[ MATH ] Mathematics [math]Jordan matrixSpectral theoryGaussian010102 general mathematicsMathematical analysisPerturbation (astronomy)Mathematics::Spectral Theory01 natural sciences010104 statistics & probabilityMatrix (mathematics)symbols.namesakesymbolsRandom perturbations[MATH]Mathematics [math]MSC: 47A10 47B80 47H40 47A550101 mathematicsDivide-and-conquer eigenvalue algorithmSpectral theoryEigenvalue perturbationEigenvalues and eigenvectorsNon-self-adjoint operatorsMathematics
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