# Remarks on nonequilibrium contributions to the rate of chemical reaction in the Lorentz gas

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- Comments on â€˜â€˜Integrals of motion for the Lorenz systemâ€™â€™ [J. Math. Phys. 34, 801 (1993)]. Cairó, L.; Hua, D. // Journal of Mathematical Physics;Sep93, Vol. 34 Issue 9, p4370
Reports on a direct method for determining the conditions under which the Lorentz system is integrable. Basis of the method on the Carleman method applied to the Lorentz system; Derivation of all integrals known for the system by Kus using the Carleman method.

- A new parametrization and all integral realizations of the Lorentz group. Louck, James D. // Journal of Mathematical Physics;Oct2002, Vol. 43 Issue 10, p5108
A simple linear transformation of the biquaternionic parameters Î± and Î² of the group SL(2, C), which is two-to-one homomorphic to the restricted Lorentz group L, is used to express each element of SL(2, C) and L in terms of the first column of an element of L and the quaternionic...

- Characterization of semidirect sum Lie algebras. Antoniou, Ioannis E.; Misra, Baidyanath // Journal of Mathematical Physics;Apr91, Vol. 32 Issue 4, p864
Semidirect sum Lie algebras A[larger_closed_square]X may be characterized by the type of the representation the invariant subalgebra X provides for the Lie algebra A. The method is of particular interest when the invariant subalgebra X is infinite dimensional and allows one to compare such...

- 1+1 solvable relativistic field models. Degasperis, A.; Tinebra, F. // Journal of Mathematical Physics;Jul93, Vol. 34 Issue 7, p2950
Nonlinear Lorentz invariant field models are constructed in such a way to be integrable by a transformation of a linear free field. The transformation is explicitly found by requiring that the U(1) conserved current keeps the same expression of the free field. This method is applied to the...

- Investigation of the Lorentz gas in terms of periodic orbits. Cvitanovic, Predrag; Gaspard, Pierre // Chaos;Jan1992, Vol. 2 Issue 1, p85
Evaluates the diffusion constant and the Lyapunov exponent for the spatially periodic Lorentz gas in terms of periodic orbits. Use of a description of the dynamics reduced to a fundamental domain to generate the shortest possible periodic orbits; Limitation of the theory when applied to dense...

- The nonequlibrium Lorentz gas. Lloyd, James; Niemeyer, Matthias; Rondoni, Lamberto; Morriss, Gary P. // Chaos;Sep95, Vol. 5 Issue 3, p536
Studies the electric conductivity of Lorentz gas groups. Diffusion coefficient of the field having well definition; Range of Periodic Orbit Expansion applied to compute the values of the thermodynamic variables; Observation of a variety of possible dynamics including the breakdown of ergodic...

- Nontrivial zeros of the Racah quadrupole invariant. Brudno, Simcha; Louck, James D. // Journal of Mathematical Physics;Jun85, Vol. 26 Issue 6, p1125
It is shown that a class of nontrivial zeros of the Racah quadrupole invariant operator is given by two orbits of the group action of an infinite discrete subgroup of the proper two-dimensional Lorentz group SO(l,1) on the hyperbola 4xÂ² - 3yÂ² = 11/4.

- The Lorentz group and the Thomas precession. II. Exact results for the product of two boosts. Salingaros, Nikos // Journal of Mathematical Physics;Jan1986, Vol. 27 Issue 1, p157
The product of two Lorentz boosts in different directions is equal to the product of a pure boost and a spatial rotation. To second order, the resulting boost is simply the sum of the individual boosts, and the rotation is responsible for the Thomas precession. Here the resulting boost and the...

- Erratum: The Lorentz group and the Thomas precession. II. Exact results for the product of two boosts [J. Math. Phys. 27, 157 (1986)]. Salingaros, N. A. // Journal of Mathematical Physics;May88, Vol. 29 Issue 5, p1265
Presents a clarification to an error in the article 'The Lorentz group and the Thomas precession. II. Exact results for the product of two boosts,' published in a 1986 issue of the 'Journal of Mathematical Physics.' Finding that there is no additional correction angle in calculating the first...