3,674 research outputs found
Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions
The monodromy transform and corresponding integral equation method described
here give rise to a general systematic approach for solving integrable
reductions of field equations for gravity coupled bosonic dynamics in string
gravity and supergravity in four and higher dimensions. For different types of
fields in space-times of dimensions with commuting isometries
-- stationary fields with spatial symmetries, interacting waves or partially
inhomogeneous cosmological models, the string gravity equations govern the
dynamics of interacting gravitational, dilaton, antisymmetric tensor and any
number of Abelian vector gauge fields (all depending only on two
coordinates). The equivalent spectral problem constructed earlier allows to
parameterize the infinite-dimensional space of local solutions of these
equations by two pairs of \cal{arbitrary} coordinate-independent holomorphic
- and - matrix functions of a spectral parameter which constitute a complete set
of monodromy data for normalized fundamental solution of this spectral problem.
The "direct" and "inverse" problems of such monodromy transform --- calculating
the monodromy data for any local solution and constructing the field
configurations for any chosen monodromy data always admit unique solutions. We
construct the linear singular integral equations which solve the inverse
problem. For any \emph{rational} and \emph{analytically matched} (i.e.
and
) monodromy data the solution for string
gravity equations can be found explicitly. Simple reductions of the space of
monodromy data leads to the similar constructions for solving of other
integrable symmetry reduced gravity models, e.g. 5D minimal supergravity or
vacuum gravity in dimensions.Comment: RevTex 7 pages, 1 figur
Integrability of generalized (matrix) Ernst equations in string theory
The integrability structures of the matrix generalizations of the Ernst
equation for Hermitian or complex symmetric -matrix Ernst potentials
are elucidated. These equations arise in the string theory as the equations of
motion for a truncated bosonic parts of the low-energy effective action
respectively for a dilaton and - matrix of moduli fields or for a
string gravity model with a scalar (dilaton) field, U(1) gauge vector field and
an antisymmetric 3-form field, all depending on two space-time coordinates
only. We construct the corresponding spectral problems based on the
overdetermined -linear systems with a spectral parameter and the
universal (i.e. solution independent) structures of the canonical Jordan forms
of their matrix coefficients. The additionally imposed conditions of existence
for each of these systems of two matrix integrals with appropriate symmetries
provide a specific (coset) structures of the related matrix variables. An
equivalence of these spectral problems to the original field equations is
proved and some approach for construction of multiparametric families of their
solutions is envisaged.Comment: 15 pages, no figures, LaTeX; based on the talk given at the Workshop
``Nonlinear Physics: Theory and Experiment. III'', 24 June - 3 July 2004,
Gallipoli (Lecce), Italy. Minor typos, language and references corrections.
To be published in the proceedings in Theor. Math. Phy
Infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations for interacting waves and inhomogeneous cosmologies
For space-times with two spacelike isometries, we present infinite
hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations
as represented by their Ernst potentials. This hierarchy contains three
arbitrary rational functions of an auxiliary complex parameter. They are
constructed using the so called `monodromy transform' approach and our new
method for the solution of the linear singular integral equation form of the
reduced Einstein equations. The solutions presented, which describe
inhomogeneous cosmological models or gravitational and electromagnetic waves
and their interactions, include a number of important known solutions as
particular cases.Comment: 7 pages, minor correction and reduction to conform with published
versio
Realistic theory of electromagnetically-induced transparency and slow light in a hot vapor of atoms undergoing collisions
We present a realistic theoretical treatment of a three-level
system in a hot atomic vapor interacting with a coupling and a probe field of
arbitrary strengths, leading to electromagnetically-induced transparency and
slow light under the two-photon resonance condition. We take into account all
the relevant decoherence processes including col5Blisions. Velocity-changing
collisions (VCCs) are modeled in the strong collision limit effectively, which
helps in achieving optical pumping by the coupling beam across the entire
Doppler profile. The steady-state expressions for the atomic density-matrix
elements are numerically evaluated to yield the experimentally measured
response characteristics. The predictions, taking into account a dynamic rate
of influx of atoms in the two lower levels of the , are in excellent
agreement with the reported experimental results for He*. The role played
by the VCC parameter is seen to be distinct from that by the transit time or
Raman coherence decay rate
Using supernova neutrinos to monitor the collapse, to search for gravity waves and to probe neutrino masses
We discuss the importance of observing supernova neutrinos. By analyzing the
SN1987A observations of Kamiokande-II, IMB and Baksan, we show that they
provide a 2.5{\sigma} support to the standard scenario for the explosion. We
discuss in this context the use of neutrinos as trigger for the search of the
gravity wave impulsive emission. We derive a bound on the neutrino mass using
the SN1987A data and argue, using simulated data, that a future galactic
supernova could probe the sub-eV region.Comment: 8 pages, 1 figure. Proceeding for the Galileo-Xu Guangqi meeting: The
Sun, the Stars, the Universe and General Relativity; October 26-30, 2009,
Shanghai (China). Accepted for publication at International Journal of Modern
Physics
Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups
In this paper, we construct a Lagrangian submanifold of the moduli space
associated to the fundamental group of a punctured Riemann surface (the space
of representations of this fundamental group into a compact connected Lie
group). This Lagrangian submanifold is obtained as the fixed-point set of an
anti-symplectic involution defined on the moduli space. The notion of
decomposable representation provides a geometric interpretation of this
Lagrangian submanifold
The Evolution of Multicomponent Systems at High Pressures: VI. The Thermodynamic Stability of the Hydrogen-Carbon System: The Genesis of Hydrocarbons and the Origin of Petroleum
The spontaneous genesis of hydrocarbons which comprise natural petroleum have
been analyzed by chemical thermodynamic stability theory. The constraints
imposed upon chemical evolution by the second law of thermodynamics are briefly
reviewed; and the effective prohibition of transformation, in the regime of
temperatures and pressures characteristic of the near-surface crust of the
Earth, of biological molecules into hydrocarbon molecules heavier than methane
is recognized.
A general, first-principles equation of state has been developed by extending
scaled particle theory (SPT) and by using the technique of the factored
partition function of the Simplified Perturbed Hard Chain Theory (SPHCT). The
chemical potentials, and the respective thermodynamic Affinity, have been
calculated for typical components of the hydrogen-carbon (H-C) system over a
range pressures between 1-100 kbar, and at temperatures consistent with those
of the depths of the Earth at such pressures. The theoretical analyses
establish that the normal alkanes, the homologous hydrocarbon group of lowest
chemical potential, evolve only at pressures greater than approximately thirty
kbar, excepting only the lightest, methane. The pressure of thirty kbar
corresponds to depths of approximately 100 km.
Special high-pressure apparatus has been designed which permits
investigations at pressures to 50 kbar and temperatures to 2000 K, and which
also allows rapid cooling while maintaining high pressures. The high-pressure
genesis of petroleum hydrocarbons has been demonstrated using only the solid
reagents iron oxide, FeO, and marble, CaCO3, 99.9% pure and wet with
triple-distilled water
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
Nonlinear dynamics and band transport in a superlattice driven by a plane wave
A quantum particle transport induced in a spatially-periodic potential by a
propagating plane wave has a number important implications in a range of
topical physical systems. Examples include acoustically driven semiconductor
superlattices and cold atoms in optical crystal. Here we apply kinetic
description of the directed transport in a superlattice beyond standard linear
approximation, and utilize exact path-integral solutions of the semiclassical
transport equation. We show that the particle drift and average velocities have
non-monotonic dependence on the wave amplitude with several prominent extrema.
Such nontrivial kinetic behaviour is related to global bifurcations developing
with an increase of the wave amplitude. They cause dramatic transformations of
the system phase space and lead to changes of the transport regime. We describe
different types of phase trajectories contributing to the directed transport
and analyse their spectral content
New Test of Supernova Electron Neutrino Emission using Sudbury Neutrino Observatory Sensitivity to the Diffuse Supernova Neutrino Background
Supernovae are rare nearby, but they are not rare in the Universe, and all
past core-collapse supernovae contributed to the Diffuse Supernova Neutrino
Background (DSNB), for which the near-term detection prospects are very good.
The Super-Kamiokande limit on the DSNB electron {\it antineutrino} flux,
cm s, is just above the
range of recent theoretical predictions based on the measured star formation
rate history. We show that the Sudbury Neutrino Observatory should be able to
test the corresponding DSNB electron {\it neutrino} flux with a sensitivity as
low as cm s,
improving the existing Mont Blanc limit by about three orders of magnitude.
While conventional supernova models predict comparable electron neutrino and
antineutrino fluxes, it is often considered that the first (and
forward-directed) SN 1987A event in the Kamiokande-II detector should be
attributed to electron-neutrino scattering with an electron, which would
require a substantially enhanced electron neutrino flux. We show that with the
required enhancements in either the burst or thermal phase fluxes, the
DSNB electron neutrino flux would generally be detectable in the Sudbury
Neutrino Observatory. A direct experimental test could then resolve one of the
enduring mysteries of SN 1987A: whether the first Kamiokande-II event reveals a
serious misunderstanding of supernova physics, or was simply an unlikely
statistical fluctuation. Thus the electron neutrino sensitivity of the Sudbury
Neutrino Observatory is an important complement to the electron antineutrino
sensitivity of Super-Kamiokande in the quest to understand the DSNB.Comment: 10 pages, 3 figure
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