Detecting photon-photon scattering in vacuum at exawatt lasers

In a recent paper, we have shown that the QED nonlinear corrections imply a phase correction to the linear evolution of crossing electromagnetic waves in vacuum. Here, we provide a more complete analysis, including a full numerical solution of the QED nonlinear wave equations for short-distance propagation in a symmetric configuration. The excellent agreement of such a solution with the result that we obtain using our perturbatively-motivated Variational Approach is then used to justify an analytical approximation that can be applied in a more general case. This allows us to find the most promising configuration for the search of photon-photon scattering in optics experiments. In particular, we show that our previous requirement of phase coherence between the two crossing beams can be released. We then propose a very simple experiment that can be performed at future exawatt laser facilities, such as ELI, by bombarding a low power laser beam with the exawatt bump.Comment: 8 pages, 6 figure

The connected components of the space of Alexandrov surfaces

Denote by $\mathcal{A}(\kappa)$ the set of all compact Alexandrov surfaces with curvature bounded below by $\kappa$ without boundary, endowed with the topology induced by the Gromov-Hausdorff metric. We determine the connected components of $\mathcal{A}(\kappa)$ and of its closure

Optical measurements of spin noise as a high resolution spectroscopic tool

The intrinsic fluctuations of electron spins in semiconductors and atomic vapors generate a small, randomly-varying "spin noise" that can be detected by sensitive optical methods such as Faraday rotation. Recent studies have demonstrated that the frequency, linewidth, and lineshape of this spin noise directly reveals dynamical spin properties such as dephasing times, relaxation mechanisms and g-factors without perturbing the spins away from equilibrium. Here we demonstrate that spin noise measurements using wavelength-tunable probe light forms the basis of a powerful and novel spectroscopic tool to provide unique information that is fundamentally inaccessible via conventional linear optics. In particular, the wavelength dependence of the detected spin noise power can reveal homogeneous linewidths buried within inhomogeneously-broadened optical spectra, and can resolve overlapping optical transitions belonging to different spin systems. These new possibilities are explored both theoretically and via experiments on spin systems in opposite limits of inhomogeneous broadening (alkali atom vapors and semiconductor quantum dots).Comment: 4 pages, 4 figure

Performance of the modified Becke-Johnson potential

Very recently, in the 2011 version of the Wien2K code, the long standing shortcome of the codes based on Density Functional Theory, namely, its impossibility to account for the experimental band gap value of semiconductors, was overcome. The novelty is the introduction of a new exchange and correlation potential, the modified Becke-Johnson potential (mBJLDA). In this paper, we report our detailed analysis of this recent work. We calculated using this code, the band structure of forty one semiconductors and found an important improvement in the overall agreement with experiment as Tran and Blaha [{\em Phys. Rev. Lett.} 102, 226401 (2009)] did before for a more reduced set of semiconductors. We find, nevertheless, within this enhanced set, that the deviation from the experimental gap value can reach even much more than 20%, in some cases. Furthermore, since there is no exchange and correlation energy term from which the mBJLDA potential can be deduced, a direct optimization procedure to get the lattice parameter in a consistent way is not possible as in the usual theory. These authors suggest that a LDA or a GGA optimization procedure is used previous to a band structure calculation and the resulting lattice parameter introduced into the 2011 code. This choice is important since small percentage differences in the lattice parameter can give rise to quite higher percentage deviations from experiment in the predicted band gap value.Comment: 10 pages, 2 figures, 5 Table

Non-equilibrium statistical mechanics of classical nuclei interacting with the quantum electron gas

Kinetic equations governing time evolution of positions and momenta of atoms in extended systems are derived using quantum-classical ensembles within the Non-Equilibrium Statistical Operator Method (NESOM). Ions are treated classically, while their electrons quantum mechanically; however, the statistical operator is not factorised in any way and no simplifying assumptions are made concerning the electronic subsystem. Using this method, we derive kinetic equations of motion for the classical degrees of freedom (atoms) which account fully for the interaction and energy exchange with the quantum variables (electrons). Our equations, alongside the usual Newtonian-like terms normally associated with the Ehrenfest dynamics, contain additional terms, proportional to the atoms velocities, which can be associated with the electronic friction. Possible ways of calculating the friction forces which are shown to be given via complicated non-equilibrium correlation functions, are discussed. In particular, we demonstrate that the correlation functions are directly related to the thermodynamic Matsubara Green's functions, and this relationship allows for the diagrammatic methods to be used in treating electron-electron interaction perturbatively when calculating the correlation functions. This work also generalises previous attempts, mostly based on model systems, of introducing the electronic friction into Molecular Dynamics equations of atoms.Comment: 18 page