On the General Theory of the Approach to Equilibrium. I. Interacting Normal Modes
1.I. Prigogine and R. Balescu, Physica 25, 281 (1959).
2.I. Prigogine and R. Balescu, Physica 25, 302 (1959).
3.L. Van Hove, Physica 21, 517 (1955).
4.The validity of this condition will be discussed by J. Philippot in a forthcoming paper.
5.λ is the coupling constant in the Hamiltonian
6.I. Prigogine and F. Henin, Physica 23, 585 (1957).
7.I. Prigogine and J. Philippot, Physica 23, 569 (1957).
8.R. Brout and I. Prigogine, Physica 22, 621 (1956).
9.The situation is the same as in the case of gases. In the equation for reduced distribution functions corresponding to a finite number of particles, the N factors disappear, while they persist if one consider equations for the whole set of variables. This comes from the simple fact that will be the order of magnitude of the time between two collisions in the master equation if τ is the time between two collisions of a given molecule.
10.We shall often drop the arrows and wave vectors of the diagrams; in that case a single diagram will represent a summation over all the diagrams which differ by the wave vectors only; the only exception will be for the lines which remain at the left of the diagram. The wave vectors of those lines are those described by the set of the Fourier component.
11.R. Peieris, Quantum Theory of Solids (Clarendon Press, Oxford, England, 1955).
12.For gases, this condition can be studied more precisely. Let us for instance consider a screened Coulomb potential. Then the Fourier coefficients are and the pole is at The condition can then be interpreted as the fact that the time t must be sufficiently large to allow the particles to travel a distance much larger than the range of the forces.
13.W. Heitler, The Quantum Theory of Radiation (Clarendon Press, Oxford, England, 1954).
14.N. N. Bogolioubov, J. Phys. U.S.S.R. 10, 265 (1946).
15.M. Kac, Probability and Related Topics in Physical Sciences (Interscience Publishers, Inc., New York, 1959), p. 132;
15.Appendix I by G. E. Uhlenbeck.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Article metrics loading...
Full text loading...