Topic
Spectrum of a matrix
About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.
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TL;DR: For a bounded planar region in R 2, Cheng and Yang as mentioned in this paper obtained the ratios of lower order eigenvalues of Laplace operator for the (k + 1 ) -th (k ⩾ 3 ) membrane eigenvalue.
24 citations
TL;DR: In this paper, the eigenvalues of an unknown density matrix of a finite-dimensional system in a single experimental setting are determined with the minimal number of parameters obtained by a measurement of a single observable.
Abstract: Eigenvalues of a density matrix characterize well the quantum state's properties, such as coherence and entanglement. We propose a simple method to determine all the eigenvalues of an unknown density matrix of a finite-dimensional system in a single experimental setting. Without fully reconstructing a quantum state, eigenvalues are determined with the minimal number of parameters obtained by a measurement of a single observable. Moreover, its implementation is illustrated in linear optical and superconducting systems.
23 citations
TL;DR: In this article, a new type of eigenvalue problem is introduced whose solution provides a spectrum of characteristic exponents for chaotic repellers or semi-attractors, and explicitly tractable examples this spectrum coincides with that of the generalized dimensions.
23 citations
TL;DR: In this paper, the authors studied a pair of neutrally stable eigenvalues of zero energy in the linearized NLS equation, where each eigenvalue has geometric multiplicity one and algebraic multiplicity N, respectively.
Abstract: We study a pair of neutrally stable eigenvalues of zero energy in the linearized NLS equation. We prove that the pair of isolated eigenvalues, where each eigenvalue has geometric multiplicity one and algebraic multiplicity N, is associated with 2P negative eigenvalues of the energy operator, where P=N∕2 if N is even and P=(N−1)∕2 or P=(N+1)∕2 if N is odd. When the potential of the linearized NLS problem is perturbed due to parameter continuations, we compute the exact number of unstable eigenvalues that bifurcate from the neutrally stable eigenvalues of zero energy.
23 citations
Journal Article•
TL;DR: In this article, the eigenvalues of Schrodinger operator with a weight on compact Riernainnian manifolds with boundary (possibly empty) and prove a general inequality for them.
Abstract: In this paper we consider eigenvalues of Schrodinger operator with a weight on compact Riernainnian manifolds with boundary (possibly empty) and prove a general inequality for them. By using this inequality, we study eigenvalues of Schrodinger operator with a weight on compact domains in a unit sphere, a complex projective space and a minimal submanifold in a Euclidean space. We also study the same problem on closed minimal submanifolds in a sphere, compact homogeneous space and closed complex hypersurfaces in a complex projective space. We give explict bound for the (k + 1)-th eigenvalue of the Schrodinger operator on such objects in terms of its first k eigenvalues. Our results generalize many previous estimates on eigenvalues of the Laplacian.
22 citations