Localization lengths and boltzmann limit for the anderson model at small disorders in dimension 3

Journal of Statistical Physics

Volumn 120, Issue 1-2, 2005, Pages 279-337

  Chen, Thomas ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Anderson model; Hydrodynamic limits; Localization lengths; Quantum kinetic theory; Random Schr dinger operators; Weak coupling limit

Indexed keywords

EID: 24644480929     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-5255-7     Document Type: Article

References (10)

1. H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger Operators (Springer Verlag, 1987).
2. L. Erdös, Linear Boltzmann equation as the scaling limit of the Schrödinger evolution coupled to a phonon bath, J. Stat. Phys. 107(5): 1043-1127 (2002).
3. L. Erdös and H.-T. Yau, Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation, Commun. Pure Appl. Math. LIII:667-753 (2000).
4. L. Erdös, M. Salmhofer, and H.-T. Yau, Quantum diffusion of the random Schrödinger evolution in the scaling limit, preprint http://xxx.lanl.gov/abs/math-ph/0502025.
5. J. Magnen, G. Poirot, and V. Rivasseau, Renormalization group methods and applications: first results for the weakly coupled Anderson model, Phys. A 263(1-4):131-140 (1999).
6. J. Magnen, G Poirot, and V. Rivasseau, Ward-type identities for the two-dimensional Anderson model at weak disorder, J. Stat. Phys. 93(1-2):331-358 (1998).
7. G. Poirot, Mean Green's function of the Anderson model at weak disorder with an infrared cut-off, Ann. Inst. H. Poincaré Phys. Théor. 70(1):101-146 (1999).
8. W. Schlag, C. Shubin, and T. Wolff, Frequency concentration and localization lengths for the Anderson model at small disorders, J. Anal. Math., 88 (2002).
9. H. Spohn, Derivation of the transport equation for electrons moving through random impurities, J. Statist. Phys., 17(6):385-412 (1977).
10. E. Stein, Harmonic Analysis (Princeton University Press, 1993).