6533b826fe1ef96bd12852a7
RESEARCH PRODUCT
Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well
Piotr GarbaczewskiMariusz ŻAbasubject
PhysicsQuantum PhysicsMathematical analysisCauchy distributionFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)EigenfunctionMathematics::Spectral TheoryDirichlet distributionMathematics - Spectral Theorysymbols.namesakeOperator (computer programming)Bound statesymbolsFOS: MathematicsA priori and a posterioriQuantum Physics (quant-ph)Spectral Theory (math.SP)Mathematical PhysicsEigenvalues and eigenvectorsShape analysis (digital geometry)description
Fractional (L\'{e}vy-type) operators are known to be spatially nonlocal. This becomes an issue if confronted with a priori imposed exterior Dirichlet boundary data. We address spectral properties of the prototype example of the Cauchy operator $(-\Delta )^{1/2}$ in the interval $D=(-1,1) \subset R$, with a focus on functional shapes of lowest eigenfunctions and their fall-off at the boundaries of $D$. New high accuracy formulas are deduced for approximate eigenfunctions. We analyze how their shape reproduction fidelity is correlated with the evaluation finesse of the corresponding eigenvalues.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-03-25 |