Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field
Erdös L. 2002. Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics. 107(5–6), 1043–1127.
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Abstract
We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear Boltzmann equation globally in time. The collision kernel is identified as the sum of an emission and an absorption term that depend on the equilibrium distribution of the free phonon modes.
Publishing Year
Date Published
2002-06-01
Journal Title
Journal of Statistical Physics
Acknowledgement
This work initially was a joint project with H.-T. Yau and several ideas
presented here have been developed in collaboration with him. I would like
to thank him for the invaluable discussions and encouragement through
the entire work. Part of this project was completed during several visits at
the Erwin Schrödinger Institute, Vienna, and at the Center of Theoretical
Studies, Hsinchu, Taiwan. The author is grateful for the hospitality and
financial support. This work was partially supported by NSF Grant DMS9970323.
Volume
107
Issue
5-6
Page
1043 - 1127
ISSN
IST-REx-ID
Cite this
Erdös L. Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics. 2002;107(5-6):1043-1127. doi:10.1023/A:1015157624384
Erdös, L. (2002). Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics. Springer. https://doi.org/10.1023/A:1015157624384
Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field.” Journal of Statistical Physics. Springer, 2002. https://doi.org/10.1023/A:1015157624384.
L. Erdös, “Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field,” Journal of Statistical Physics, vol. 107, no. 5–6. Springer, pp. 1043–1127, 2002.
Erdös L. 2002. Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics. 107(5–6), 1043–1127.
Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field.” Journal of Statistical Physics, vol. 107, no. 5–6, Springer, 2002, pp. 1043–127, doi:10.1023/A:1015157624384.
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