Randomly chosen chaotic maps can give rise to nearly ordered behavior

Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226–5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72], the resulting composed map has a periodic orbit which is stable.     

Yang-Lee zeros of a planar Ising model with a boundary magnetic field

A planar Ising ferromagnet is investigated with a magnetic field acting on one surface. The Yang-Lee zeros associated with this field are located exactly on the imaginary axis and their limiting distribution is given. Above the critical temperature, this distribution has a gap, near which the pair correlation for spins in the surface exhibits cirtical behaviour. The zeros of certain antiferromagnets are located, in particular those for an antiferromagnetic ring coupled ferromagnetically to a planar Ising ferromagnet.On leave from: University of Oxford. Current Address: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712, USA     

Signatures of non-Abelian statistics in nonlinear Coulomb blockade transport

Signatures of the non-Abelian statistics of quasiparticles in the ν=5/2 quantum Hall state are predicted to be present in the current-voltage characteristics of tunneling through one or two quantum Hall puddles of Landau filling ν(a) embedded in a bulk of filling ν(b) with (ν(a),ν(b))=(2,5/2) and (ν(a),ν(b))=(5/2,2).     

Dual-wavelength laser source for onboard atom interferometry

We present a compact and stable dual-wavelength laser source for onboard atom interferometry with two different atomic species. It is based on frequency-doubled telecom lasers locked on a femtosecond optical frequency comb. We take advantage of the maturity of fiber telecom technology to reduce the number of free-space optical components, which are intrinsically less stable, and to make the setup immune to vibrations and thermal fluctuations. The source provides the frequency agility and phase stability required for atom interferometry and can easily be adapted to other cold atom experiments. We have shown its robustness by achieving the first dual-species K-Rb magneto-optical trap in microgravity during parabolic flights.     

Vacuum decay constraints on a cosmological scalar field

If the potential of a scalar field phi which currently provides the "dark energy" of the Universe has a minimum at phi = -M(0)(4)<0, then quantum-mechanical fluctuations could nucleate a bubble of phi at a negative value of the potential. This bubble would then expand at the speed of light. Given that no such bubble enveloped us in the past, we find that any minimum in V(phi) must be separated from the current phi value by more than min[1.5M(0),0.21M(Pl)], where M(Pl) is the Planck mass. We also show that vacuum decay renders a cyclic or ekpyrotic universe with M(0)(4) > or approximately 10(-10)M(4)(Pl) untenable.     

Witten Spinors on Nonspin Manifolds

Motivated by Witten’s spinor proof of the positive mass theorem, we analyze asymptotically constant harmonic spinors on complete asymptotically flat nonspin manifolds with nonnegative scalar curvature.