Linear Boltzmann equation as scaling limit of quantum Lorentz gas
Erdös L, Yau H. 1998.Linear Boltzmann equation as scaling limit of quantum Lorentz gas. In: Advances in Differential Equations and Mathematical Physics. Contemporary Mathematics, vol. 217, 137–155.
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Book Chapter
| Published
| English
Author
Erdös, LászlóISTA 
;
Yau, Horng
;
Yau, HorngSeries Title
Contemporary Mathematics
Abstract
We study a quantum particle in a random potential in two scaling limits: the low density limit (or Boltzman-Grad) and the weak coupling limit. The low density limit is the quantum analogue of the Lorentz gas. In both cases, the phase space density of the quantum evolution defined through the Wigner transform or the Husimi function converges weakly to a linear Boltz-mann equation with collision kernel given by the quantum scattering cross section.
Publishing Year
Date Published
1998-01-01
Book Title
Advances in Differential Equations and Mathematical Physics
Volume
217
Page
137 - 155
ISSN
IST-REx-ID
Cite this
Erdös L, Yau H. Linear Boltzmann equation as scaling limit of quantum Lorentz gas. In: Advances in Differential Equations and Mathematical Physics. Vol 217. American Mathematical Society; 1998:137-155. doi:10.1090/conm/217
Erdös, L., & Yau, H. (1998). Linear Boltzmann equation as scaling limit of quantum Lorentz gas. In Advances in Differential Equations and Mathematical Physics (Vol. 217, pp. 137–155). American Mathematical Society. https://doi.org/10.1090/conm/217
Erdös, László, and Horng Yau. “Linear Boltzmann Equation as Scaling Limit of Quantum Lorentz Gas.” In Advances in Differential Equations and Mathematical Physics, 217:137–55. American Mathematical Society, 1998. https://doi.org/10.1090/conm/217.
L. Erdös and H. Yau, “Linear Boltzmann equation as scaling limit of quantum Lorentz gas,” in Advances in Differential Equations and Mathematical Physics, vol. 217, American Mathematical Society, 1998, pp. 137–155.
Erdös L, Yau H. 1998.Linear Boltzmann equation as scaling limit of quantum Lorentz gas. In: Advances in Differential Equations and Mathematical Physics. Contemporary Mathematics, vol. 217, 137–155.
Erdös, László, and Horng Yau. “Linear Boltzmann Equation as Scaling Limit of Quantum Lorentz Gas.” Advances in Differential Equations and Mathematical Physics, vol. 217, American Mathematical Society, 1998, pp. 137–55, doi:10.1090/conm/217.
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