2,844 research outputs found
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
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
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
Dynamical boundary conditions for integrable lattices
Some special solutions to the reflection equation are considered. These
boundary matrices are defined on the common quantum space with the other
operators in the chain. The relations with the Drinfeld twist are discussed.Comment: LaTeX, 12page
Physical phase space of lattice Yang-Mills theory and the moduli space of flat connections on a Riemann surface
It is shown that the physical phase space of \g-deformed Hamiltonian
lattice Yang-Mills theory, which was recently proposed in refs.[1,2], coincides
as a Poisson manifold with the moduli space of flat connections on a Riemann
surface with handles and therefore with the physical phase space of
the corresponding -dimensional Chern-Simons model, where and are
correspondingly a total number of links and vertices of the lattice. The
deformation parameter \g is identified with and is an
integer entering the Chern-Simons action.Comment: 12 pages, latex, no figure
Boundary three-point function on AdS2 D-branes
Using the H3+-Liouville relation, I explicitly compute the boundary
three-point function on AdS2 D-branes in H3+, and check that it exhibits the
expected symmetry properties and has the correct geometrical limit. I then find
a simple relation between this boundary three-point function and certain fusing
matrix elements, which suggests a formal correspondence between the AdS2
D-branes and discrete representations of the symmetry group. Concluding
speculations deal with the fuzzy geometry of AdS2 D-branes, strings in the
Minkowskian AdS3, and the hypothetical existence of new D-branes in H3+.Comment: 27 pages, v2: significant clarifications added in sections 4.3 and
Laser in the axial electric field as a tool to search for P-, T- invariance violation
We consider rotation of polarization plane of the laser light when a gas
laser is placed in a longitudinal electric field (10~kV/cm). It is shown that
residual anisotropy of the laser cavity 10^{-6} and the sensitivity to the
angle of polarization plane rotation about 10^{-11} -10^{-12} rad allows one to
measure an electron EDM with the sensitivity about 10^{-30} e cm.Comment: 12 page
Fully Electrified Neugebauer Spacetimes
Generalizing a method presented in an earlier paper, we express the complex
potentials E and Phi of all stationary axisymmetric electrovac spacetimes that
correspond to axis data of the form E(z,0) = (U-W)/(U+W) , Phi(z,0) = V/(U+W) ,
where U = z^{2} + U_{1} z + U_{2} , V = V_{1} z + V_{2} , W = W_{1} z + W_{2} ,
in terms of the complex parameters U_{1}, V_{1}, W_{1}, U_{2}, V_{2} and W_{2},
that are directly associated with the various multipole moments. (Revised to
clarify certain subtle points.)Comment: 25 pages, REVTE
Spontaneous DC Current Generation in a Resistively Shunted Semiconductor Superlattice Driven by a TeraHertz Field
We study a resistively shunted semiconductor superlattice subject to a
high-frequency electric field. Using a balance equation approach that
incorporates the influence of the electric circuit, we determine numerically a
range of amplitude and frequency of the ac field for which a dc bias and
current are generated spontaneously and show that this region is likely
accessible to current experiments. Our simulations reveal that the Bloch
frequency corresponding to the spontaneous dc bias is approximately an integer
multiple of the ac field frequency.Comment: 8 pages, Revtex, 3 Postscript figure
Suppressed absolute negative conductance and generation of high-frequency radiation in semiconductor superlattices
We show that space-charge instabilities (electric field domains) in
semiconductor superlattices are the attribute of absolute negative conductance
induced by small constant and large alternating electric fields. We propose the
efficient method for suppression of this destructive phenomenon in order to
obtain a generation at microwave and THz frequencies in devices operating at
room temperature. We theoretically proved that an unbiased superlattice with a
moderate doping subjected to a microwave pump field provides a strong gain at
third, fifth, seventh, etc. harmonics of the pump frequency in the conditions
of suppressed domains.Comment: 8 pages. Development of cond-mat/0503216 . Version 2: Final version,
erratum is include
- …