In this correspondence we derive the asymptotic distribution of the MUSIC null spectrum, from which an exact expression of the asymptotic variance of the MUSIC null spectrum can be obtained. The result presented in this correspondence is a simpler alternative and a special case of a more general result recently obtained by Lee and Wengrovitz.

The spectrum of anyons confined in harmonic oscillator potential shows both linear and nonlinear dependence on the statistical parameter. While the existence of exact linear solutions have been shown analytically, the nonlinear dependence has been arrived at by numerical and/or perturbative methods. We develop a method which shows the possibility of nonlinearly interpolating spectrum. To be spe...

The slopes of maximal subbundles of rank s divided by the degree of the map under various pull backs form a bounded collection of numbers called the s-spectrum of the bundle. We study the supremum of the s-spectrum and determine it in terms of the Harder Narasimhan filtration of the bundle.

We establish an asymptotic formula, uniformly down to the Planck scale, for number of small gaps between first N eigenvalues Laplacian on almost all flat tori and also rectangular tori.

We investigate the relation between the four dimensional N = 2 SU(2) super Yang-Mills theory with four fundamental flavors and the quantum mechanics model with Treibich-Verdier potential described by the Heun equation in the elliptic form. We study the precise correspondence of quantities in the gauge theory and the quantum mechanics model. An iterative method is used to obtain the asymptotic e...

The operator H = d 4 dt4 + d dt p d dt + q with periodic coefficients p, q on the real line is considered. The spectrum of H is absolutely continuous and consists of intervals separated by gaps. The following statements are proved: 1) the endpoints of gaps are periodic or antiperiodic eigenvalues or branch points of the Lyapunov function, and moreover, their asymptotic behavior at high energy i...