A review of the decoherent histories approach to the arrival time problem in quantum theory

We review recent progress in understanding the arrival time problem in quantum mechanics, from the point of view of the decoherent histories approach to quantum theory. We begin by discussing the arrival time problem, focussing in particular on the role of the probability current in the expected classical solution. After a brief introduction to decoherent histories we review the use of complex potentials in the construction of appropriate class operators. We then discuss the arrival time problem for a particle coupled to an environment, and review how the arrival time probability can be expressed in terms of a POVM in this case. We turn finally to the question of decoherence of the corresponding histories, and we show that this can be achieved for simple states in the case of a free particle, and for general states for a particle coupled to an environment.Comment: 10 pages. To appear in DICE 2010 conference proceeding

The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition

We analytically derive the spectrum of gravitational waves due to magneto-hydrodynamical turbulence generated by bubble collisions in a first-order phase transition. In contrast to previous studies, we take into account the fact that turbulence and magnetic fields act as sources of gravitational waves for many Hubble times after the phase transition is completed. This modifies the gravitational wave spectrum at large scales. We also model the initial stirring phase preceding the Kolmogorov cascade, while earlier works assume that the Kolmogorov spectrum sets in instantaneously. The continuity in time of the source is relevant for a correct determination of the peak position of the gravitational wave spectrum. We discuss how the results depend on assumptions about the unequal-time correlation of the source and motivate a realistic choice for it. Our treatment gives a similar peak frequency as previous analyses but the amplitude of the signal is reduced due to the use of a more realistic power spectrum for the magneto-hydrodynamical turbulence. For a strongly first-order electroweak phase transition, the signal is observable with the space interferometer LISA.Comment: 46 pages, 17 figures. Replaced with revised version accepted for publication in JCA

Symmetric coupling of four spin-1/2 systems

We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free subsystems. We provide a detailed analysis of the coupling of three and four spin-1/2 systems and discuss a symmetric coupling of four spin-1/2 systems.Comment: 20 pages, no figure

Stochastic String Motion Above and Below the World Sheet Horizon

We study the stochastic motion of a relativistic trailing string in black hole AdS_5. The classical string solution develops a world-sheet horizon and we determine the associated Hawking radiation spectrum. The emitted radiation causes fluctuations on the string both above and below the world-sheet horizon. In contrast to standard black hole physics, the fluctuations below the horizon are causally connected with the boundary of AdS. We derive a bulk stochastic equation of motion for the dual string and use the AdS/CFT correspondence to determine the evolution a fast heavy quark in the strongly coupled $\N=4$ plasma. We find that the kinetic mass of the quark decreases by $\Delta M=-\sqrt{\gamma \lambda}T/2$ while the correlation time of world sheet fluctuations increases by $\sqrt{\gamma}$.Comment: 27 pages, 5 figures; v2 final version, small changes, references adde

Supersymmetric Axion-Neutrino Merger

The recently proposed supersymmetric $A_4$ model of the neutrino mass matrix is modified to merge with a previously proposed axionic solution of the strong CP problem. The resulting model has only one input scale, i.e. that of $A_4$ symmetry breaking, which determines both the seesaw neutrino mass scale and the axion decay constant. It also solves the $\mu$ problem and conserves R parity automatically.Comment: 7 pages, no figur

The Neutrino Mass Matrix - New Developments

With the recent experimental advance in our precise knowledge of the neutrino oscillation parameters, the correct form of the 3 X 3 neutrino mass matrix is now approximately known. I discuss how this may be obtained from symmetry principles, using as examples the finite groups A_4 and Z_4, predicting as a result three nearly degenerate Majorana neutrino masses in the 0.2 eV range.Comment: 14 pages, talk at BEYOND 200