High-energy cutoff in the spectrum of strong-field nonsequential double ionization

Electron energy distributions of singly and doubly ionized helium in an intense 390 nm laser field have been measured at two intensities (0.8 PW/cm(2) and 1.1 PW/cm(2), where PW equivalent to 10(15) W/cm(2)). Numerical solutions of the full-dimensional time-dependent helium Schrodinger equation show excellent agreement with the experimental measurements. The high-energy portion of the two-electron energy distributions reveals an unexpected 5U(p) cutoff for the double ionization (DI) process and leads to a proposed model for DI below the quasiclassical threshold.

The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

The Essential Role of Human Databases for Learning in and Validation of Affectively Competent Agents.

This output is an invited and refereed chapter in the second of the two book length outputs resulting from the EU HUMAINE grant and follow-on grants. The book is in the OUP Affective Science Series and is intended to provide a theoretically oriented state of the art model for those working in the area of affective computing. Each chapter provides a synthesis of a specific area and presents new data/findings/approaches developed by the author(s) which take the area further. This chapter is in the section on ‘Approaches to developing expression corpora and databases.’ The chapter provides a critical synthesis of the issues involved in databases for affective computing and introduces the SEMAINE SAL Database, developed as an integral part of the EU SEMAINE Project (The Sensitive Agent Project 2008-2011) which is an interdisciplinary project. The project aimed to develop a computer interface that would allow a human to interact with an artificial agent in an emotional manner.

On the spectrum of frequently hypercyclic operators

A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question.

Infrared spectrum of an extremely cool white-dwarf star

White dwarfs are the remnant cores of stars that initially had masses of less than 8 solar masses. They cool gradually over billions of years, and have been suggested(1,2) to make up much of the 'dark matter' in the halo of the Milky way. But extremely cool white dwarfs have proved difficult to detect, owing to both their faintness and their anticipated similarity in colour to other classes of dwarf stars. Recent improved models(3-5) indicate that white dwarfs are much more blue than previously supposed, suggesting that the earlier searches may have been looking for the wrong kinds of objects. Here we report an infrared spectrum of an extremely cool white dwarf that is consistent with the new models. We determine the star's temperature to be 3,500 +/- 200 K, making it the coolest known white dwarf. The kinematics of this star indicate that it is in the halo of the Milky Way, and the density of such objects implied by the serendipitous discovery of this star is consistent with white dwarfs dominating the dark matter in the halo.

Dense spectrum of resonances and particle capture in a near-black-hole metric

We show that a quantum scalar particle in the gravitational field of a massive body of radius R which slightly exceeds the Schwarzschild radius rs, possesses a dense spectrum of narrow resonances. Their lifetimes and density tend to infinity in the limit R?rs. We determine the cross section of the particle capture into these resonances and show that it is equal to the absorption cross section for a Schwarzschild black hole. Thus, a nonsingular static metric acquires black-hole properties before the actual formation of a black hole.