Tag: Eigenvalues and eigenvectors
Defective atomic lattice enables unidirectional reflection lasing
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in OpticsWhat the study found The study reports a scheme for mode-tunable unidirectional reflection lasing using a coherent gain atomic system and a one-dimensional defective atomic lattice. The authors describe this as a single system that combines nonreciprocity and lasing oscillation. Why the authors say this matters The authors say the approach could improve the efficiency…
Generic cuspidal points can be localized from eigenvalue loops
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in MathematicsWhat the study found The study finds that generic cuspidal points, meaning parameter values where eigenvalues coalesce in smooth complex-valued matrix functions of two parameters, can be analyzed through loops in parameter space. It also states that phase accumulation for eigenvectors can occur around such loops, and that eigenvalue periodicity and phase accumulation may help…
Radial perturbations give spherical harmonic eigenfunctions in impedance tomography
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in MathematicsWhat the study found The study found that, for rotationally symmetric conductivity perturbations in the unit ball, the eigenfunctions of the linearized electrical impedance tomography operator correspond to spherical harmonics. It also gives an explicit formula for the associated eigenvalues. Why the authors say this matters The authors conclude that the structure they establish is…
Weighted Neumann eigenvalues are established for outward cuspidal domains
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in MathematicsWhat the study found The study establishes Sobolev-space embeddings into weighted Lebesgue spaces for a nonlinear Neumann eigenvalue problem in outward cuspidal domains. These embeddings are used to show solvability of the Neumann spectral problem and to estimate the associated weighted Neumann eigenvalues. Why the authors say this matters The authors say these embedding results…
