Towards a Quantum Analog of Weak KAM Theory

Communications in Mathematical Physics

Volumn 244, Issue 2, 2004, Pages 311-334

  Evans, Lawrence C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0842281980     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0975-5     Document Type: Article

References (21)

1. [A] Ananlharaman, N.: Gibbs measures on path space and viscous approximation to action-minimizing measures. Trans. AMS, 2003
2. [B-L-P] Bensoussan, A., Lions, J.-L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures, Amsterdam: North-Holland, 1978
3. [Cpl Capdeboscq, Y.: Homogenization of a neutronic critical diffusion problem with drift. Proc. Royal Soc. Edinburgh 132, 567-594 (2002)
4. [C] Carlen, E.: Conservative diffusions. Commun. Math. Phys. 94, 293-315 (1984)
5. [E1] Evans, L.C.: Effective Hamiltonians and quantum states. Seminaire Equations aux Dérivées Partielles, Ecole Polytechnique 2000-2001
6. [E2] Evans, L.C.: Some new PDE methods for weak KAM theory. Calculus of Variations and PDE 17, 159-177 (2003)
7. [E-G] Evans, L.C., Gomes, D.: Effective Hamiltonians and averaging for Hamiltonian Dynamics I. Arch. Rat. Mech. Anal. 157, 1-33 (2001)
8. [F1] Fathi, A.: Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens. C. R. Acad. Sci. Paris Sr. 1 Math. 324, 1043-1046 (1997)
9. [F2] Fathi, A.: Solutions KAM faibles conjuguèes et barrières de Peierls. C. R. Acad. Sci. Paris Sr. I Math. 325, 649-652 (1997)
10. [F3] Fathi, A.: Weak KAM theory in Lagrangian Dynamics, Preliminary Version. Lecture notes 2001
11. [G] Gomes, D.: A stochastic analogue of Aubry-Mather theory. Nonlinearity 15, 581-603 (2002)
12. [G-M] Guerra, F., Morato, L.: Quantization of dynamical systems and stochastic control theory. Phys. Rev. D 27, 1774-1786 (1983)
13. [H-K] Holcman, D., Kupka, I.: Singular perturbations and first order PDE on manifolds. Preprint, 2002
14. [L-P-V] Lions, P.-L., Papanicolaou, G., Varadhan, S. R. S.: Homogenization of Hamilton-Jacobi equations. Unpublished, circa 1988
15. [M1] Mather, J.: Minimal measures. Comment. Math Helv. 64, 375-394 (1989)
16. [M2] Mather, J.: Action minimizing invariant measures for positive definite Lagrangian systems. Math. Zeits. 207, 169-207 (1991)
17. [M-F] Mather, J., Forni, G.: Action minimizing orbits in Hamiltonian systems. In: Transition to Chaos in Classical and Quantum Mechanics, Lecture Notes in Math 1589, S. Graffi ed., Berlin-Heidelberg-New York: Springer, 1994
18. [N] Nelson, E.: Quantum Fluctuations. Princeton, NJ: Princeton University Press, 1985
19. [P] Pedersen, F.B.: Simple derivation of the effective mass equation using a multiple-scale technique. Euro. J. Phys. 18, 43-45 (1997)
20. [Ya] Yasue, K.: Stochastic calculus of variations. J. Funct. Anal. 41, 327-340 (1981)
21. [Y] Yu, Y.: Error estimates for a quantization of a Mather set. To appear