1,602 research outputs found
The calculation of TV, VT, VV, VV' ? rate coefficients for the collisions of the main atmospheric components
International audienceThe first-order perturbation approximation is applied to calculate the rate coefficients of vibrational energy transfer in collisions involving vibrationally excited molecules in the absence of non-adiabatic transitions. The factors of molecular attraction, oscillator frequency change, anharmonicity, 3-dimensionality and quasiclassical motion have been taken into account in the approximation. The analytical expressions presented have been normalized on experimental data of VT-relaxation times in N2 and O2 to obtain the steric factors and the extent of repulsive exchange potentials in collisions N2-N2 and O2-O2. The approach was applied to calculate the rate coefficients of vibrational-vibrational energy transfer in the collisions N2-N2, O2-O2 and N2-O2. It is shown that there is good agreement between our calculations and experimental data for all cases of energy transfer considered
A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups
We give a description of the (small) quantum cohomology ring of the flag
variety as a certain commutative subalgebra in the tensor product of the
Nichols algebras. Our main result can be considered as a quantum analog of a
result by Y. Bazlov
Ground state and low excitations of an integrable chain with alternating spins
An anisotropic integrable spin chain, consisting of spins and
, is investigated \cite{devega}. It is characterized by two real
parameters and , the coupling constants of the spin
interactions. For the case and the ground state
configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore
the low excitations are calculated. It turns out, that apart from free magnon
states being the holes in the ground state rapidity distribution, there exist
bound states given by special string solutions of Bethe ansatz equations (BAE)
in analogy to \cite{babelon}. The dispersion law of these excitations is
calculated numerically.Comment: 16 pages, LaTeX, uses ioplppt.sty and PicTeX macro
Quasi-Isotropization of the Inhomogeneous Mixmaster Universe Induced by an Inflationary Process
We derive a ``generic'' inhomogeneous ``bridge'' solution for a cosmological
model in the presence of a real self-interacting scalar field. This solution
connects a Kasner-like regime to an inflationary stage of evolution and
therefore provides a dynamical mechanism for the quasi-isotropization of the
universe. In the framework of a standard Arnowitt-Deser-Misner Hamiltonian
formulation of the dynamics and by adopting Misner-Chitr\`e-like variables, we
integrate the Einstein-Hamilton-Jacobi equation corresponding to a ``generic''
inhomogeneous cosmological model whose evolution is influenced by the coupling
with a bosonic field, expected to be responsible for a spontaneous symmetry
breaking configuration. The dependence of the detailed evolution of the
universe on the initial conditions is then appropriately characterized.Comment: 17 pages, no figure, to appear on PR
Quantum Interaction : the Construction of Quantum Field defined as a Bilinear Form
We construct the solution of the quantum wave equation
as a bilinear form which can
be expanded over Wick polynomials of the free -field, and where
is defined as the normal ordered product with
respect to the free -field. The constructed solution is correctly defined
as a bilinear form on , where is a
dense linear subspace in the Fock space of the free -field. On
the diagonal Wick symbol of this bilinear form
satisfies the nonlinear classical wave equation.Comment: 32 pages, LaTe
Combinatorics of -orbits and Bruhat--Chevalley order on involutions
Let be the group of invertible upper-triangular complex
matrices, the space of upper-triangular complex matrices with
zeroes on the diagonal and its dual space. The group acts
on by , , ,
.
To each involution in , the symmetric group on letters, one
can assign the -orbit . We present a
combinatorial description of the partial order on the set of involutions
induced by the orbit closures. The answer is given in terms of rook placements
and is dual to A. Melnikov's results on -orbits on .
Using results of F. Incitti, we also prove that this partial order coincides
with the restriction of the Bruhat--Chevalley order to the set of involutions.Comment: 27 page
Gauging of Geometric Actions and Integrable Hierarchies of KP Type
This work consist of two interrelated parts. First, we derive massive
gauge-invariant generalizations of geometric actions on coadjoint orbits of
arbitrary (infinite-dimensional) groups with central extensions, with gauge
group being certain (infinite-dimensional) subgroup of . We show that
there exist generalized ``zero-curvature'' representation of the pertinent
equations of motion on the coadjoint orbit. Second, in the special case of
being Kac-Moody group the equations of motion of the underlying gauged WZNW
geometric action are identified as additional-symmetry flows of generalized
Drinfeld-Sokolov integrable hierarchies based on the loop algebra {\hat \cG}.
For {\hat \cG} = {\hat {SL}}(M+R) the latter hiearchies are equivalent to a
class of constrained (reduced) KP hierarchies called {\sl cKP}_{R,M}, which
contain as special cases a series of well-known integrable systems (mKdV, AKNS,
Fordy-Kulish, Yajima-Oikawa etc.). We describe in some detail the loop algebras
of additional (non-isospectral) symmetries of {\sl cKP}_{R,M} hierarchies.
Apart from gauged WZNW models, certain higher-dimensional nonlinear systems
such as Davey-Stewartson and -wave resonant systems are also identified as
additional symmetry flows of {\sl cKP}_{R,M} hierarchies. Along the way we
exhibit explicitly the interrelation between the Sato pseudo-differential
operator formulation and the algebraic (generalized) Drinfeld-Sokolov
formulation of {\sl cKP}_{R,M} hierarchies. Also we present the explicit
derivation of the general Darboux-B\"acklund solutions of {\sl cKP}_{R,M}
preserving their additional (non-isospectral) symmetries, which for R=1 contain
among themselves solutions to the gauged WZNW field
equations.Comment: LaTeX209, 47 page
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