Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

A remark on the semi-classical measure from $ {-{h^2\over 2}\Delta +V}$ with a degenerate potential $ V$

Author(s): Yifeng Yu
Journal: Proc. Amer. Math. Soc. 135 (2007), 1449-1454.
MSC (2000): Primary 35P20
Posted: November 13, 2006
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: This note is motivated by Evans (2004) and Anantharaman (2004). We study the semiclassical measure arising from the operator $ P(h)=-{h^2\over 2}\Delta +V(x)$ when the potential $ V$ has degenerate minimum points. We will use the technique of integration by parts and some identities of Evans to derive information on the support of the measure.

References:

[A]
N. Anantharaman, On the zero-temperature or vanishing viscosity limit for certain Markov processes arising from Lagrangian dynamics., J. Eur. Math. Soc. (JEMS) 6 (2004), no. 2, 207-276. MR 2055035 (2005i:82004)

[D-S]
M. Dimassi, J. Sjöstrand, Spectral Asymptotics in the Semi-Classical Limit, Cambridge University Press, 1999. MR 1735654 (2001b:35237)

[E1]
L.C. Evans, Toward a quantum analogue of weak KAM theory, Comm. Math. Phys. 244 (2004), no. 2, 311-334. MR 2031033 (2005c:81063)

[E2]
L.C. Evans, Some new PDE methods for weak KAM theory, Calc. Var. Partial Differential Equations 17 (2003), no. 2, 159-177. MR 1986317 (2004e:37097)

[E3]
L.C. Evans, Effective Hamiltonians and quantum states, Seminaire Equations aux Dérivées Partielles, Ecole Polytechnique (2000-2001). MR 1860693 (2002j:81049)

[E-Z]
L.C. Evans, M. Zworski, Lectures on semiclassical analysis, Lecture note.

[H]
B. Helffer, Semi-classical analysis for the Schr$ \ddot o$dinger operator and applications, Springer Lect. Notes in Math., 1336 (1988). MR 0960278 (90c:81043)

[J-K-M]
H.R. Jauslin, H.O. Kreiss, J. Moser, On the forced Burgers equation with periodic boundary conditions, Proc. Symposia in Pure Math 65, 133-153, 1999. MR 1662751 (99m:35208)

[Y]
Y. Yu, $ L^{\infty}$ variational problems, Aronsson equations and weak KAM theory, Ph.D. dissertation, U.C. Berkeley(2005).

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35P20

Retrieve articles in all Journals with MSC (2000): 35P20

Additional Information:

Yifeng Yu
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: yifengyu@math.berkeley.edu

DOI: 10.1090/S0002-9939-06-08702-8
PII: S 0002-9939(06)08702-8
Received by editor(s): December 19, 2005
Posted: November 13, 2006
Communicated by: Mikhail Shubin
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google