Abstract
The continuous spectrum of the linear Boltzmann operator with constant field is derived. It is found that a sufficiency relation for runaway phenomena is consistent with another sufficiency relation for the hydrodynamic regime to exist. There is a further class of systems whose behavior lies in between these two extremes.
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References
K. Kumar, The physics of swarms and some basic questions of kinetic theory,Phys. Rep. 112:321 (1984).
H. Grad, Asymptotic theory of the Boltzmann equation ii, inRarified Gas Dynamics, J. A. Laurmann, ed. (Academic Press, New York, 1963).
Y. Pao,Commun. Pure Appl. Math. 27:407 (1974).
B. Nicolaenko, Dispersion laws for plane wave propagation, inThe Boltzmann Equation, F. A. Grünbaum, ed. (Courant Institute, New York University, New York, 1972).
C. Cercignani,The Boltz mann Equation and its Applications (Springer, New York, 1988).
H. Weyl, On ordinary differential equations with singularities and the associated expansions of arbitrary functions,Math. Ann. 68:220–269 (1910).
Martin Schecter, On the essential spectrum of an arbitrary operator. i,J. Math. Anal. Appl. 13:205–215 (1966).
František Wolf, On the essential spectrum of partial differential boundary problems,Commun. Pure Appl. Math. 12:211–228 (1959).
R. Standish, Non-hydrodynamic contributions to the end effects in time of flight swarm experiments,Aust. J. Phys. 40:519 (1987).
G. Cavalleri and S. L. Paveri-Fontana, Drift velocity and runaway phenomena for electrons in neutral gases,Phys. Rev. A 5:327 (1972).
Giovanni Frosali, Cornelius V. M. van der Mee, and Stefano L. Paveri-Fontana, Conditions for runaway phenomena in the kinetic theory of swarms,J. Math. Phys. 30:1177–1186 (1989).
M. Waldman and E. A. Mason, On the density dependence of runaway mobility,Chem. Phys. Lett. 83:369–371 (1981).
F. Howorka, F. C. Fehsenfeld, and D. L. Albritton,J. Phys. B 12:4189 (1979).
J. L. Morruzzi and Y. Kondo,Jpn. J. Appl. Phys. 19:1411 (1980).
K. F. Ness and R. Robson, Transport properties of electrons in water vapour,Phys. Rev. A 38:1446 (1988).
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Standish, R.K. On the spectrum of the linear Boltzmann operator. J Stat Phys 66, 1003–1010 (1992). https://doi.org/10.1007/BF01055713
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DOI: https://doi.org/10.1007/BF01055713