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Comments on Kinetic Equation for Autocorrelation Functions
1.See, for instance, P. Résibois, J. Chem. Phys. 41, 2979 (1964), and references quoted therein.
2.R. Zwanzig, Phys. Rev. 124, 983 (1961).
3.B. Berne, J. P. Boon, and S. Rice, J. Chem. Phys. 45, 1086 (1966).
4.I. Prigogine, Non‐Equilibrium Statistical Mechanics (Interscience Publishers, Inc., New York, 1962).
5.P. Résibois, in Many‐Particle Physics, E. Meeron, Ed. (Gordon & Breach Science Publishers, Inc., New York, 1967).
6.See, respectively, Refs. 2 and 3.
7.See Ref. 5, as well as H. Terwiel and P. Mazur, Physica 32, 1813 (1966);
7.P. Mazur and H. Terwiel, Physica 36, 289 (1967).
8.See especially, I. Prigogine and R. Balescu, Physica 23, 555 (1957).
9.R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. I (Interscience Publishers, Inc., New York, 1953). Note that all equations are written here for a discrete spectrum.
9.Because of the very fast decay of the initial condition (3.9) at infinity, this result appears to be correct in view of recent rigorous analysis [see C. H. Su, J. Math. Phys. 8, 148 (1967)]. However, our conclusions would be unaffected if the continuous spectrum of contributed to the evolution of
10.M. Baus, Bull. Acad. Sci. Belg. 53, 1291 (1967).
11.A pathological case is found when one tries to expand as a virial series, in power of the density ρ; the well‐known divergence in the virial expansion of the transport coefficients is related to a logarithmic singularity of at the origin
12.See Ref. 3 and A. Rahman, Phys. Rev. 136, A405 (1964).
13.It is gratefully acknowledged that the matter of this appendix is the result of fruitful discussions with Dr. M. De Leener.
14.See, for instance, G. Sansone and J. Gerretsen, Lecture on the Theory of Functions of a Complex Variable (P. Noordhoff Ltd., Groningen, The Netherlands, 1960).
15.We assume here strictly speaking, instead of (All) we have the case is, however, trivial to treat.
16.We see here that the asymptotic result (A22) is valid for finite, satisfying (A11). We do not know, however, whether this condition (A11) is very restrictive or not.
17.P. Résibois and H. T. Davis, Physica 30, 1077 (1964).
18.P. Dirac, The Principles of Quantum Mechanics (Oxford University Press, London, 1947), 3rd ed.
19.The factor 2 in front of the delta function arises because we adopt the convention
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