Multiplicative Dirac structures on Lie groups

We study multiplicative Dirac structures on Lie groups. We show that the characteristic foliation of a multiplicative Dirac structure is given by the cosets of a normal Lie subgroup and, whenever this subgroup is closed, the leaf space inherits the structure of a Poisson-Lie group. We also describe multiplicative Dirac structures on Lie groups infinitesimally.Comment: Published in Comptes Rendus Mathematiqu

Contact manifolds and generalized complex structures

We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.Comment: 12 pages, typos correcte

Relativistic magnetohydrodynamics in one dimension

We derive a number of solution for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: system of highly non-linear, relativistic, time dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.Comment: accepted by Phys. Rev.

Sometimes Close is Good Enough: The Value of Nearby Environmental Amenities

An extensive empirical literature exists showing that variations in region-specific amenities can account for persistent differences in real wages across regions. However, this literature has considered only amenities in the same location as the household. This paper argues that environmental amenities at some distance from but accessible to urban areas may lead to negative compensating wage differentials. We use a general equilibrium framework and data from the 1995 Current Population Survey to calculate implicit amenity prices based on measures of distance to environmental amenities. Our results suggest that amenities outside the metropolitan area do generate compensating wage differentials, as workers are willing to accept lower wages to live in accessible proximity to “nice” places. This implies that these places provide a positive externality to those communities that find them accessible. The estimated effects are quantitatively important, suggesting that these externalities should be taken into account in policy making.

Semiclassical Expansions, the Strong Quantum Limit, and Duality

We show how to complement Feynman's exponential of the action so that it exhibits a Z_2 duality symmetry. The latter illustrates a relativity principle for the notion of quantum versus classical.Comment: 5 pages, references adde

A Developmental Approach for low-level Imitations

Historically, a lot of authors in psychology and in robotics tend to separate "true imitation" and its related high-level mechanisms which seem to be exclusive to human adult, from low-level imitations or "mimicries" observed on babies or primates. Closely, classical researches suppose that an imitative artificial system must be able to build a model of the demonstrator's geometry, in order to reproduce finely the movements on each joints. Conversely, we will advocate that if imitation is viewed as a part of a developmental course, then (1) an artificial developing system does not need to build any internal model of the other, to perform real-time and low-level imitations of human movements despite the related correspondence problem between man and robot and, (2) a simple sensory-motor loop could be at the basis of multiples heterogeneous imitative behaviors often explained in the literature by different models

A Quantum-Gravity Perspective on Semiclassical vs. Strong-Quantum Duality

It has been argued that, underlying M-theoretic dualities, there should exist a symmetry relating the semiclassical and the strong-quantum regimes of a given action integral. On the other hand, a field-theoretic exchange between long and short distances (similar in nature to the T-duality of strings) has been shown to provide a starting point for quantum gravity, in that this exchange enforces the existence of a fundamental length scale on spacetime. In this letter we prove that the above semiclassical vs. strong-quantum symmetry is equivalent to the exchange of long and short distances. Hence the former symmetry, as much as the latter, also enforces the existence of a length scale. We apply these facts in order to classify all possible duality groups of a given action integral on spacetime, regardless of its specific nature and of its degrees of freedom.Comment: 10 page

Fixed point theorem for simple quantum strategies in quantum market games

A simple but nontrivial class of the quantum strategies in buying-selling games is presented. The player moves are a rational buying and an unconditional selling. The possibility of gaining extremal profits in such the games is considered. The entangled merchants hypothesis is proposed.Comment: 7 pages, 1 figure; The International Econophysics Conference, Bali 200

Twistor spaces of generalized complex structures

The twistor construction is applied for obtaining examples of generalized complex structures (in the sense of N. Hitchin) that are not induced by a complex or a symplectic structure.Comment: revised version, 17 pages; corrected typos, added references, minor stylistic changes in the expositio

Skyrmion on a three--cylinder

The class of static, spherically symmetric, and finite energy hedgehog solutions in the SU(2) Skyrme model is examined on a metric three-cylinder. The exact analytic shape function of the 1-Skyrmion is found. It can be expressed via elliptic integrals. Its energy is calculated, and its stability with respect to radial and spherically symmetric deformations is analyzed. No other topologically nontrivial solutions belonging to this class are possible on the three-cylinder.Comment: v2: version accepted for publication in Phys. Rev.