Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

Optical Transistor for an Amplification of Radiation in a Broadband THz Domain

We propose a new type of optical transistor for a broadband amplification of THz radiation. It is made of a graphene--superconductor hybrid, where electrons and Cooper pairs couple by Coulomb forces. The transistor operates via the propagation of surface plasmons in both layers, and the origin of amplification is the quantum capacitance of graphene. It leads to THz waves amplification, the negative power absorption, and as a result, the system yields positive gain, and the hybrid acts like an optical transistor, operating with the terahertz light. It can, in principle, amplify even a whole spectrum of chaotic signals (or noise), that is required for numerous biological applications.Comment: 7 pages, 3 figure

Observables for spacetimes with two Killing field symmetries

The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed directly in the Hamiltonian theory. The reduced system corresponds to the field equations of the SL(2,R) chiral model with additional constraints. On the classical phase space, a method of obtaining an infinite number of constants of the motion, or observables, is given. The procedure involves writing the Hamiltonian evolution equations as a single `zero curvature' equation, and then employing techniques used in the study of two dimensional integrable models. Two infinite sets of observables are obtained explicitly as functionals of the phase space variables. One set carries sl(2,R) Lie algebra indices and forms an infinite dimensional Poisson algebra, while the other is formed from traces of SL(2,R) holonomies that commute with one another. The restriction of the (complex) observables to the Euclidean and Lorentzian sectors is discussed. It is also shown that the sl(2,R) observables can be associated with a solution generating technique which is linked to that given by Geroch.Comment: 23 pages (LateX-RevTeX), Alberta-Thy-55-9

Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the ``null-curvature'' equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. These spaces of solutions of the ``null-curvature'' equations can be parametrized by a finite sets of free functional parameters -- arbitrary holomorphic (in some local domains) functions of the spectral parameter which can be interpreted as the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. Direct and inverse problems of such mapping (``monodromy transform''), i.e. the problem of finding of the monodromy data for any local solution of the ``null-curvature'' equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problems and the explicit forms of the monodromy data corresponding to the spaces of solutions of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction

A non-perturbative method of calculation of Green functions

A new method for non-perturbative calculation of Green functions in quantum mechanics and quantum field theory is proposed. The method is based on an approximation of Schwinger-Dyson equation for the generating functional by exactly soluble equation in functional derivatives. Equations of the leading approximation and the first step are solved for $\phi^4_d$-model. At $d=1$ (anharmonic oscillator) the ground state energy is calculated. The renormalization program is performed for the field theory at $d=2,3$. At $d=4$ the renormalization of the coupling involves a trivialization of the theory.Comment: 13 pages, Plain LaTex, no figures, some discussion of results for anharmonic oscillator and a number of references are added, final version published in Journal of Physics

Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem

We consider the collisions of plane gravitational and electromagnetic waves with distinct wavefronts and of arbitrary polarizations in a Minkowski background. We first present a new, completely geometric formulation of the characteristic initial value problem for solutions in the wave interaction region for which initial data are those associated with the approaching waves. We present also a general approach to the solution of this problem which enables us in principle to construct solutions in terms of the specified initial data. This is achieved by re-formulating the nonlinear dynamical equations for waves in terms of an associated linear problem on the spectral plane. A system of linear integral ``evolution'' equations which solve this spectral problem for specified initial data is constructed. It is then demonstrated explicitly how various colliding plane wave space-times can be constructed from given characteristic initial data.Comment: 33 pages, 3 figures, LaTeX. Accepted for publication in Classical and Quantum Gravit

The Ecology and Evolution of Patience in Two New World Monkeys

Decision making often involves choosing between small, short-term rewards and large, long-term rewards. All animals, humans included, discount future rewards-the present value of delayed rewards is viewed as less than the value of immediate rewards. Despite its ubiquity, there exists considerable but unexplained variation between species in their capacity to wait for rewards-that is, to exert patience or self-control. Using two closely related primates-common marmosets (Callithrix jacchus) and cotton-top tamarins (Saguinus oedipus)-we uncover a variable that may explain differences in how species discount future rewards. Both species faced a self-control paradigm in which individuals chose between taking an immediate small reward and waiting a variable amount of time for a large reward. Under these conditions, marmosets waited significantly longer for food than tamarins. This difference cannot be explained by life history, social behaviour or brain size. It can, however, be explained by feeding ecology: marmosets rely on gum, a food product acquired by waiting for exudate to flow from trees, whereas tamarins feed on insects, a food product requiring impulsive action. Foraging ecology, therefore, may provide a selective pressure for the evolution of self-control.Psycholog

Chiral corrections to the isovector double scattering term for the pion-deuteron scattering length

The empirical value of the real part of the pion-deuteron scattering length can be well understood in terms of the dominant isovector $\pi N$-double scattering contribution. We calculate in chiral perturbation theory all one-pion loop corrections to this double scattering term which in the case of $\pi N$-scattering close the gap between the current-algebra prediction and the empirical value of the isovector threshold T-matrix $T_{\pi N}^-$. In addition to closing this gap there is in the $\pi d$-system a loop-induced off-shell correction for the exchanged virtual pion. Its coordinate space representation reveals that it is equivalent to $2\pi$-exchange in the deuteron. We evaluate the chirally corrected double scattering term and the off-shell contribution with various realistic deuteron wave functions. We find that the off-shell correction contributes at most -8% and that the isovector double scattering term explains at least 90% of the empirical value of the real part of the $\pi d$-scattering length.Comment: 4 pages, 2 figures, to be published in The Physical Review

Measurements of the composition of aerosol component of Venusian atmosphere with Vega 1 lander, preliminary data

Preliminary investigation of mass spectra of gaseous products of pyrolyzed Venusian cloud particles collected and analyzed by the complex device of mass-spectrometer and collector pyrolyzer on board Vega 1 lander revealed the presence of heavy particles in the upper cloud layer. Based on 64 amu peak (SO2+), an estimate of the lower limit of the sulfuric acid aerosol content at the 62 to 54 km heights of approximately 2.0 mg/cu m is obtained. A chlorine line (35 and 37 amu) is also present in the mass spectrum with a lower limit of the chlorine concentration of approximately 0.3 mg/ cu m

Techniques for the study of singularities with applications to resolution of 2-dimensional schemes

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.Comment: 26 pages; minor changes have been adde