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

Effects related to spacetime foam in particle physics

It is found that the existence of spacetime foam leads to a situation in which the number of fundamental quantum bosonic fields is a variable quantity. The general aspects of an exact theory that allows for a variable number of fields are discussed, and the simplest observable effects generated by the foam are estimated. It is shown that in the absence of processes related to variations in the topology of space, the concept of an effective field can be reintroduced and standard field theory can be restored. However, in the complete theory the ground state is characterized by a nonvanishing particle number density. From the effective-field standpoint, such particles are "dark". It is assumed that they comprise dark matter of the universe. The properties of this dark matter are discussed, and so is the possibility of measuring the quantum fluctuation in the field potentials.Comment: 18 pages, minor corrections added to the published varian

Ground state and low excitations of an integrable chain with alternating spins

An anisotropic integrable spin chain, consisting of spins $s=1$ and $s=\frac{1}{2}$, is investigated \cite{devega}. It is characterized by two real parameters $\bar{c}$ and $\tilde{c}$, the coupling constants of the spin interactions. For the case $\bar{c}<0$ and $\tilde{c}<0$ 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

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

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 $G$ with central extensions, with gauge group $H$ being certain (infinite-dimensional) subgroup of $G$. 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 $G$ 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 $N$-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 $SL(M+1)/U(1)\times SL(M)$ WZNW field equations.Comment: LaTeX209, 47 page

Quantum Interaction ϕ44\phi^4_4: the Construction of Quantum Field defined as a Bilinear Form

We construct the solution $\phi(t,{\bf x})$ of the quantum wave equation $\Box\phi + m^2\phi + \lambda:\!\!\phi^3\!\!: = 0$ as a bilinear form which can be expanded over Wick polynomials of the free $in$-field, and where $:\!\phi^3(t,{\bf x})\!:$ is defined as the normal ordered product with respect to the free $in$-field. The constructed solution is correctly defined as a bilinear form on $D_{\theta}\times D_{\theta}$, where $D_{\theta}$ is a dense linear subspace in the Fock space of the free $in$-field. On $D_{\theta}\times D_{\theta}$ the diagonal Wick symbol of this bilinear form satisfies the nonlinear classical wave equation.Comment: 32 pages, LaTe

Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.

We present a complete study of boundary bound states and related boundary S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our approach is based partly on the bootstrap procedure, and partly on the explicit solution of the inhomogeneous XXZ model with boundary magnetic field and of the boundary Thirring model. We identify boundary bound states with new ``boundary strings'' in the Bethe ansatz. The boundary energy is also computed.Comment: 25 pages, harvmac macros Report USC-95-001