Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
41 (2000), S. 4478-4496
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Phase space tunneling and exponential decay of eigenfunctions in phase space are well known for operators with symbols which are analytic in some neighborhood of the real axis. This can be used to prove an adiabatic theorem of exponential order if one assumes the Hamiltonian to depend analytically on time. However to study compactly supported switching processes one has to weaken the analyticity assumptions. Here we examine nonanalytic symbols with Gevrey class regularity and show that we get an exponential decay of the corresponding eigenfunctions with respect to (h-dash-bar)1/a as (h-dash-bar)→0, where a〉1. The loss of regularity causes a slower decay in (h-dash-bar). The analysis is done using the methods of Martinez and its generalization by Nakamura. An upper bound for the rate of decay is given. © 2000 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.533355
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