scholarly journals An approximate formula for the diffusion coefficient for the periodic Lorentz gas

2012 ◽  
Vol 376 (23) ◽  
pp. 1819-1822 ◽  
Author(s):  
C. Angstmann ◽  
G.P. Morriss
Keyword(s):  
Diffusion Coefficient ◽  
Approximate Formula ◽  
Lorentz Gas ◽  
Periodic Lorentz Gas

CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL

1988 ◽  
Vol 02 (01) ◽  
pp. 103-120 ◽  
Author(s):  
AVRAHAM COHEN ◽  
SHMUEL FISHMAN
Keyword(s):  
Diffusion Coefficient ◽  
Classical Limit ◽  
Approximate Formula ◽  
Quantum Systems ◽  
Potential Well ◽  
Diffusive Growth ◽  
Classical Chaos ◽  
The One ◽  
Short Time ◽  
Infinite Potential Well

The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

scholarly journals Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas

2012 ◽  
Vol 146 (6) ◽  
pp. 1221-1243 ◽  
Author(s):  
Federico Bonetto ◽  
Nikolai Chernov ◽  
Alexey Korepanov ◽  
Joel L. Lebowitz
Keyword(s):  
Spatial Structure ◽  
Lorentz Gas ◽  
Stationary Nonequilibrium States ◽  
Periodic Lorentz Gas ◽  
Nonequilibrium States

On the Distribution of Free Path Lengths¶for the Periodic Lorentz Gas

1998 ◽  
Vol 190 (3) ◽  
pp. 491-508 ◽  
Author(s):  
Jean Bourgain ◽  
François Golse ◽  
Bernt Wennberg
Keyword(s):  
Free Path ◽  
Lorentz Gas ◽  
Periodic Lorentz Gas ◽  
Path Lengths ◽  
Free Path Lengths

Diffusion in a Periodic Lorentz Gas

1983 ◽  
Vol 50 (25) ◽  
pp. 1959-1962 ◽  
Author(s):  
Jonathan Machta ◽  
Robert Zwanzig
Keyword(s):  
Lorentz Gas ◽  
Periodic Lorentz Gas
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