5,752 research outputs found
Integrability of the symmetry reduced bosonic dynamics and soliton generating transformations in the low energy heterotic string effective theory
Integrable structure of the symmetry reduced dynamics of massless bosonic
sector of the heterotic string effective action is presented. For string
background equations that govern in the space-time of dimensions ()
the dynamics of interacting gravitational, dilaton, antisymmetric tensor and
any number of Abelian vector gauge fields, all depending only on two
coordinates, we construct an \emph{equivalent} matrix
spectral problem (). This spectral problem provides the base for the
development of various solution constructing procedures (dressing
transformations, integral equation methods). For the case of the absence of
Abelian gauge fields, we present the soliton generating transformations of any
background with interacting gravitational, dilaton and the second rank
antisymmetric tensor fields. This new soliton generating procedure is available
for constructing of various types of field configurations including stationary
axisymmetric fields, interacting plane, cylindrical or some other types of
waves and cosmological solutions.Comment: 4 pages; added new section on Belinski-Zakharov solitons and new
expressions for calculation of the conformal factor; corrected typo
Soliton Nature of Equilibrium State of Two Charged Masses in General Relativity
New derivation of static equilibrium state for two charged masses in General
Relativity is given in the framework of the Inverse Scattering Method as an
alternative to our previous derivation of this solution by the Integral
Equation Method. This shows that such solution is of solitonic character and
represents the particular case of more general (12-parametric) stationary
axisymmetric electrovacuum two-soliton solution for two rotating charged
objects obtained by one of the authors in 1986. This result gives an additional
support to our comprehension that the appropriate analytical continuations of
solitonic solutions in the space of their parameters are always possible and
that applicability of the Inverse Scattering Method in presence of
electromagnetic field is not restricted only to the cases with naked
singularities.Comment: 7 pages, RevTeX
Representation Theory of Chern Simons Observables
Recently we suggested a new quantum algebra, the moduli algebra, which was
conjectured to be a quantum algebra of observables of the Hamiltonian Chern
Simons theory. This algebra provides the quantization of the algebra of
functions on the moduli space of flat connections on a 2-dimensional surface.
In this paper we classify unitary representations of this new algebra and
identify the corresponding representation spaces with the spaces of conformal
blocks of the WZW model. The mapping class group of the surface is proved to
act on the moduli algebra by inner automorphisms. The generators of these
automorphisms are unitary elements of the moduli algebra. They are constructed
explicitly and proved to satisfy the relations of the (unique) central
extension of the mapping class group.Comment: 63 pages, late
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
Superposition of fields of two Reissner - Nordstrom sources
In this paper we present a 5-parametric family of static asymptotically flat
solutions for the superposed gravitational and electromagnetic fields of two
Reissner-Nordstr\"om sources with arbitrary parameters -- masses, charges and
separating distance. A procedure for solving of the linear singular integral
equation form of the electrovacuum Einstein - Maxwell equations for stationary
axisymmetric fields is described in detail. The 4-parametric family of
equilibrium configurations of two Reissner-Nordstr\"om sources (one of which
should be a black hole and another one -- a naked singularity) presented in our
recent paper \cite{Alekseev-Belinski:2007} arises after a restriction of the
parameters of the 5-parametric solution presented here by the equilibrium
condition which provides the absence in the solution of conical points on the
symmetry axis between the sources.Comment: 24 pages, submitted to the Proceedings of the Eleventh Marcel
Grossmann Meeting (Berlin, July 23 - 29, 2006
Optical chaos in nonlinear photonic crystals
We examine a spatial evolution of lightwaves in a nonlinear photonic crystal
with a quadratic nonlinearity when simultaneously a second harmonic and a
sum-frequency generation are quasi-phase-matched. We find the conditions of a
transition to Hamiltonian chaos for different amplitudes of lightwaves at the
boundary of the crystal.Comment: LaTEX2e, 5 pages, 4 figure
Direct current generation due to harmonic mixing: From bulk semiconductors to semiconductor superlattices
We discuss an effect of dc current and dc voltage (stopping bias) generation
in a semiconductor superlattice subjected by an ac electric field and its
phase-shifted n-th harmonic. In the low field limit, we find a simple
dependence of dc voltage on a strength, frequency, and relative phase of mixing
harmonics for an arbitrary even value of n.
We show that the generated dc voltage has a maximum when a frequency of ac
field is of the order of a scattering constant of electrons in a superlattice.
This means that for typical semiconductor superlattices at room temperature
operating in the THz frequency domain the effect is really observable.
We also made a comparison of a recent paper describing an effect of a
directed current generation in a semiconductor superlattice subjected by ac
field and its second harmonic (n=2) [K.Seeger, Appl.Phys.Lett. 76(2000)82] with
our earlier findings describing the same effect [K.Alekseev et al., Europhys.
Lett. 47(1999)595; cond-mat/9903092 ].
For the mixing of an ac field and its n-th harmonic with n>=4, we found that
additionally to the phase-shift controlling of the dc current, there is a
frequency control. This frequency controlling of the dc current direction is
absent in the case of n=2. The found effect is that, both the dc current
suppression and the dc current reversals exist for some particular values of ac
field frequency. For typical semiconductor superlattices such an interesting
behavior of the dc current should be observable also in the THz domain.
Finally, we briefly review the history of the problem of the dc current
generation at mixing of harmonics in semiconductors and semiconductor
microstructures.Comment: 9 pages, 1 figure, RevTEX, EPS
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