14,645 research outputs found
Riccati parameter modes from Newtonian free damping motion by supersymmetry
We determine the class of damped modes \tilde{y} which are related to the
common free damping modes y by supersymmetry. They are obtained by employing
the factorization of Newton's differential equation of motion for the free
damped oscillator by means of the general solution of the corresponding Riccati
equation together with Witten's method of constructing the supersymmetric
partner operator. This procedure leads to one-parameter families of (transient)
modes for each of the three types of free damping, corresponding to a
particular type of %time-dependent angular frequency. %time-dependent,
antirestoring acceleration (adding up to the usual Hooke restoring
acceleration) of the form a(t)=\frac{2\gamma ^2}{(\gamma t+1)^{2}}\tilde{y},
where \gamma is the family parameter that has been chosen as the inverse of the
Riccati integration constant. In supersymmetric terms, they represent all those
one Riccati parameter damping modes having the same Newtonian free damping
partner modeComment: 6 pages, twocolumn, 6 figures, only first 3 publishe
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.
Pure-radiation gravitational fields with a simple twist and a Killing vector
Pure-radiation solutions are found, exploiting the analogy with the Euler-
Darboux equation for aligned colliding plane waves and the Euler-Tricomi
equation in hydrodynamics of two-dimensional flow. They do not depend on one of
the spacelike coordinates and comprise the Hauser solution as a special
subcase.Comment: revtex, 9 page
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
U-Duality and Symplectic Formulation of Dilaton-Axion Gravity
We study a bosonic four--dimensional effective action corresponding to the
heterotic string compactified on a 6--torus (dilaton--axion gravity with one
vector field) on a curved space--time manifold possessing a time--like Killing
vector field. Previously an existence of the global
symmetry (--duality) as well as the symmetric space property of the
corresponding --model have been established following Neugebauer and
Kramer approach. Here we present an explicit form of the generators
in terms of coset variables and construct a representation of the coset in
terms of the physical target space coordinates. Complex symmetric
matrix (``matrix dilaton --axion'') is introduced for which --duality
takes the matrix valued form. In terms of this matrix the theory is
further presented as a K\"ahler --model. This leads to a more concise
formulation which opens new ways to construct exact classical
solutions. New solution (corresponding to constant ) is obtained
which describes the system of point massless magnetic monopoles endowed with
axion charges equal to minus monopole charges. In such a system mutual magnetic
repulsion is exactly balanced by axion attraction so that the resulting space
time is locally flat but possesses multiple Taub--NUT singularities.Comment: LATEX, 20 pages, no figure
Constants of motion for vacuum general relativity
The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting
spacelike Killing vector fields, may be written as the equations of the
principal chiral model with certain `source' terms. Using this
formulation, we give a procedure for generating an infinite number of non-local
constants of motion for this sector of the Einstein equations. The constants of
motion arise as explicit functionals on the phase space of Einstein gravity,
and are labelled by sl(2,R) indices.Comment: 10 pages, latex, version to appear in Phys. Rev. D
New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors
A new first integral for the equations corresponding to twisting type-N
vacuum gravitational fields with two non-commuting Killing vectors is
introduced. A new reduction of the problem to a complex second-order ordinary
differential equation is given. Alternatively, the mentioned first integral can
be used in order to provide a first integral of the second-order complex
equation introduced in a previous treatment of the problem.Comment: 7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in
Class. Quantum Gra
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 -double
scattering contribution. We calculate in chiral perturbation theory all
one-pion loop corrections to this double scattering term which in the case of
-scattering close the gap between the current-algebra prediction and the
empirical value of the isovector threshold T-matrix . In addition
to closing this gap there is in the -system a loop-induced off-shell
correction for the exchanged virtual pion. Its coordinate space representation
reveals that it is equivalent to -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 -scattering length.Comment: 4 pages, 2 figures, to be published in The Physical Review
Solution generating with perfect fluids
We apply a technique, due to Stephani, for generating solutions of the
Einstein-perfect fluid equations. This technique is similar to the vacuum
solution generating techniques of Ehlers, Harrison, Geroch and others. We start
with a ``seed'' solution of the Einstein-perfect fluid equations with a Killing
vector. The seed solution must either have (i) a spacelike Killing vector and
equation of state P=rho or (ii) a timelike Killing vector and equation of state
rho+3P=0. The new solution generated by this technique then has the same
Killing vector and the same equation of state. We choose several simple seed
solutions with these equations of state and where the Killing vector has no
twist. The new solutions are twisting versions of the seed solutions
Switching dynamics between metastable ordered magnetic state and nonmagnetic ground state - A possible mechanism for photoinduced ferromagnetism -
By studying the dynamics of the metastable magnetization of a statistical
mechanical model we propose a switching mechanism of photoinduced
magnetization. The equilibrium and nonequilibrium properties of the Blume-Capel
(BC) model, which is a typical model exhibiting metastability, are studied by
mean field theory and Monte Carlo simulation. We demonstrate reversible changes
of magnetization in a sequence of changes of system parameters, which would
model the reversible photoinduced magnetization. Implications of the calculated
results are discussed in relation to the recent experimental results for
prussian blue analogs.Comment: 12 pages, 13 figure
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