Semilinear response for the heating rate of cold atoms in vibrating traps

The calculation of the heating rate of cold atoms in vibrating traps requires a theory that goes beyond the Kubo linear response formulation. If a strong "quantum chaos" assumption does not hold, the analysis of transitions shows similarities with a percolation problem in energy space. We show how the texture and the sparsity of the perturbation matrix, as determined by the geometry of the system, dictate the result. An improved sparse random matrix model is introduced: it captures the essential ingredients of the problem, and leads to a generalized variable range hopping picture.Comment: 6 pages, 6 figures, improved version to be published in Europhysics Letter

An Extended Relevance Model for Session Search

The session search task aims at best serving the user's information need given her previous search behavior during the session. We propose an extended relevance model that captures the user's dynamic information need in the session. Our relevance modelling approach is directly driven by the user's query reformulation (change) decisions and the estimate of how much the user's search behavior affects such decisions. Overall, we demonstrate that, the proposed approach significantly boosts session search performance

A characterization of convex cones of matrices with constant regular inertia

AbstractLet A be a convex cone of n×n matrices. In this paper, we present a necessary and sufficient condition for A to contain matrices with a constant regular inertia, based on a version of the Lyapunov equation. The condition involves only the normalized extreme points of A. This extends a previous paper by the authors, where a robust stability criterion for A was obtained

Maximal rank Hermitian completions of partially specified hermitian matrices

AbstractIn this note it is shown that, for a given partially specified hermitian matrix P, the maximal rank for arbitrary (possibly nonhermitian, complex) completions can be attained by hermitian completions. A simple formula for the maximal rank for nonhermitian completions was computed previously by Cohen et al. We also discuss the same situation for symmetric matrices over an arbitrary field, and show that the field size may be critical in establishing the same formulas. Finally, we discuss the same questions under Toeplitz structure, and show that for the matrixH=1?1?1?1?1the maximal completion rank is 3 for complex hermitian Toeplitz completions, 3 for real symmetric completions, 3 for real Toeplitz completions, but only 2 for real symmetric Toeplitz completions

The Lyapunov order for real matrices

AbstractThe real Lyapunov order in the set of real n×n matrices is a relation defined as follows: A⩽B if, for every real symmetric matrix S, SB+BtS is positive semidefinite whenever SA+AtS is positive semidefinite. We describe the main properties of the Lyapunov order in terms of linear systems theory, Nevenlinna–Pick interpolation and convexity