Secondary homotopy groups

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic models of homotopy types with homotopy groups concentrated in two consecutive dimensions.Comment: We added further commets and references to make the paper more easily readabl

Optical Pumping of TeH+: Implications for the Search for Varying mp/me

Molecular overtone transitions provide optical frequency transitions sensitive to variation in the proton-to-electron mass ratio ($\mu\equiv m_p/m_e$). However, robust molecular state preparation presents a challenge critical for achieving high precision. Here, we characterize infrared and optical-frequency broadband laser cooling schemes for TeH$^+$, a species with multiple electronic transitions amenable to sustained laser control. Using rate equations to simulate laser cooling population dynamics, we estimate the fractional sensitivity to $\mu$ attainable using TeH$^+$. We find that laser cooling of TeH$^+$ can lead to significant improvements on current $\mu$ variation limits

Evolution Operators for Linearly Polarized Two-Killing Cosmological Models

We give a general procedure to obtain non perturbative evolution operators in closed form for quantized linearly polarized two Killing vector reductions of general relativity with a cosmological interpretation. We study the representation of these operators in Fock spaces and discuss in detail the conditions leading to unitary evolutions.Comment: Accepted for publication in Physical Review

Effectively four-dimensional spacetimes emerging from d=5 Einstein-Gauss-Bonnet Gravity

Einstein-Gauss-Bonnet gravity in five-dimensional spacetime provides an excellent example of a theory that, while including higher-order curvature corrections to General Relativity, still shares many of its features, such as second-order field equations for the metric. We focus on the largely unexplored case where the coupling constants of the theory are such that no constant-curvature solution is allowed, leaving open the question of what the vacuum state should then be. We find that even a slight deviation from the anti-de Sitter Chern-Simons theory, where the vacuum state is five-dimensional AdS spacetime, leads to a complete symmetry breakdown, with the fifth dimension either being compactified into a small circle or shrinking away exponentially with time. A complete family of solutions, including duality relations among them, is uncovered and shown to be unique within a certain class. This dynamical dimensional reduction scenario seems particularly attractive as a means for higher-dimensional theories to make contact with our four-dimensional world.Comment: 9 pages, 4 figures. v2: New section on geometrical significance of solutions. Final version for CQ

Rotating Dilaton Solutions in 2+1 Dimensions

We report a three parameter family of solutions for dilaton gravity in 2+1 dimensions with finite mass and finite angular momentum. These solutions are obtained by a compactification of vacuum solutions in 3+1 dimensions with cylindrical symmetry. One class of solutions corresponds to conical singularities and the other leads to curvature singularities.Comment: Accepted to be published in Gen. Rel. Grav., added reference

Entanglement dynamics in presence of diversity under decohering environments

We study the evolution of entanglement of a pair of coupled, non-resonant harmonic oscillators in contact with an environment. For both the cases of a common bath and of two separate baths for each of the oscillators, a full master equation is provided without rotating wave approximation. This allows us to characterize the entanglement dynamics as a function of the diversity between the oscillators frequencies and their mutual coupling. Also the correlation between the occupation numbers is considered to explore the degree of quantumness of the system. The singular effect of the resonance condition (identical oscillators) and its relationship with the possibility of preserving asymptotic entanglement are discussed. The importance of the bath's memory properties is investigated by comparing Markovian and non-Markovian evolutions

The Pricing Behaviour of Firms in the Euro Area: New Survey Evidence

This study investigates the pricing behaviour of firms in the euro area on the basis of surveys conducted by nine Eurosystem national central banks. Overall, more than 11,000 firms participated in the survey. The results are very robust across countries. Firms operate in monopolistically competitive markets, where prices are mostly set following mark-up rules and where price discrimination is a common practice. Our evidence suggests that both time- and state-dependent pricing strategies are applied by firms in the euro area: around one-third of the companies follow mainly time-dependent pricing rules while two-thirds use pricing rules with some element of state-dependence. Although the majority of firms take into account a wide range of information, including past and expected economic developments, about one-third adopts a purely backward-looking behaviour. The pattern of results lends support to the recent wave of estimations of hybrid versions of the New Keynesian Phillips Curve. Price stickiness arises both at the stage when firms review their prices and again when they actually change prices. The most relevant factors underlying price rigidity are customer relationships – as expressed in the theories about explicit and implicit contracts – and thus, are mainly found at the price changing (second) stage of the price adjustment process. Finally, we provide evidence that firms adjust prices asymmetrically in response to shocks, depending on the direction of the adjustment and the source of the shock: while cost shocks have a greater impact when prices have to be raised than when they have to be reduced, reductions in demand are more likely to induce a price change than increases in demand.