We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum (−∞,−1] ∪ [1,∞). The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a ...

We study the existence, uniqueness and rate of decay of correlation of equilibrium measures associated to robust classes of non-uniformly expanding local diffeomorphisms and Hölder continuous potentials. The approach used in this paper is the spectral analysis of the Ruelle-PerronFrobenius transfer operator. More precisely, we combine the expanding features of the eigenmeasures of the transfer ...

We study some similarities between almost product Riemannian structures and almost Hermitian structures. Inspired by the similarities, we prove lower eigenvalue estimates for the Dirac operator on compact Riemannian spin manifolds with locally product structures. We also provide some examples (limiting manifolds) for the limiting case of the estimates. MSC(2000): 53C25, 53C27, 58B20

We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the socalled Gross-Pitaevskii (GP) limit of a dilute gas. Analyzing both the absolute and the bosonic ground state of the system we show, in particular, their different behavior for a certain range of p...

In this paper we consider the hermitian extension of the cross-ΨB-energy operator that we will denote by ΨH . In addition, cross energy terms are formalized through multivariate signals representation. We investigate the connection between the interaction energy function of ΨH and the cross-power spectral density (CPSD) of two complex valued signals. In particular, this link permits to use this...

In this paper, we propose a theoretical scheme for the generation of non-classical states of the cavity field in a system of a single trapped atom via controlling the Lamb-Dicke parameter. By exploiting the super-operator method, we obtain an analytical expression for the density operator of the system by which we examine the dynamical behaviors of the atomic population inversion, the phase-spa...

Surveys of clusters of galaxies provide us with a powerful probe of the density and nature of the dark energy. The red-shift distribution of detected clusters is highly sensitive to the dark energy equation of state parameter w. Upcoming Sunyaev– Zel’dovich (SZ) surveys would provide us large yields of clusters to very high red-shifts. Self-calibration of cluster scaling relations, possible for...

• Notation. What will here be called density operators are often (as in CQT) referred to as density matrices. Alas, a “density matrix” is not always a matrix, and has nothing whatsoever to do with “density” in the usual meaning of that term. Thus the term “density operator,” which only suffers from the second of these defects, is to be preferred. ⋆ Mathematical definition: any operator ρ on the...