TY  - JOUR
A1  - Bär, Christian
A1  - Pfaeffle, Frank
T1  - Asymptotic heat kernel expansion in the semi-classical limit
N2  - Let H-h = h(2)L + V, where L is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and V is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of H-h as h SE arrow 0. As a consequence we get an asymptotic expansion for the quantum partition function and we see that it is asymptotic to the classical partition function. Moreover, we show how to bound the quantum partition function for positive h by the classical partition function.
Y1  - 2010
UR  - http://www.springerlink.com/content/100467
U6  - https://doi.org/10.1007/s00220-009-0973-3
SN  - 0010-3616
ER  - 
TY  - JOUR
A1  - Bär, Christian
A1  - Bessa, C. Pacelli
T1  - Stochastic completeness and volume growth
N2  - It was suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This is motivated by a large class of examples and by a known analogous criterion for recurrence of Brownian motion. We show that the suggested implication is not true in general. We also give counterexamples to a converse implication.
Y1  - 2010
UR  - http://www.ams.org/proc/
U6  - https://doi.org/10.1090/S0002-9939-10-10281-0
SN  - 0002-9939
ER  -