منابع مشابه
On Trace Formulas
We review a variety of recently obtained trace formulas for one-and multi-dimensional Schrr odinger operators. Some of the results are extended to Sturm-Liouville and matrix-valued Schrr odinger operators. Furthermore, we recall a set of trace formulas in one, two, and three dimensions related to point interactions as well as a new uniqueness result for three-dimensional Schrr odinger operators...
متن کاملGeometrization of Trace Formulas
Recently, a new approach to functoriality of automorphic representations [L1] has been proposed in [FLN] following earlier work [L2, L3, L4] by Robert Langlands. The idea may be roughly summarized as follows. Let G and H be two reductive algebraic groups over a global field F (which is either a number field or a function field; that is, the field of functions on a smooth projective curve X over...
متن کاملTrace formulas 16
Dynamics is posed in terms of local equations, but the ergodic averages require global information. How can we use a local description of a flow to learn something about the global behavior? We have given a quick sketch of this program in Sections 1.5 and 1.6; now we redo the same material in greater depth. In Chapter 15 we have related global averages to the eigenvalues of appropriate evolutio...
متن کاملAccuracy of Trace Formulas
Using quantum maps we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy, in some systems, is demonstrated quantitatively. However, our study of the standard map cautions that this may not be most general. While studying a sawtooth map we demonstrate the rather remarkable fact that at the level of the time one trace even in the presence...
متن کاملSemiclassical trace formulas for pitchfork bifurcation sequences.
In nonintegrable Hamiltonian systems with mixed phase space and discrete symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way from integrability to chaos. In extending the semiclassical trace formula for the spectral density, we develop a uniform approximation for the combined contribution of pitchfork bifurcation pairs. For a two-dimensional double-well potential and...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2001
ISSN: 1029-8479
DOI: 10.1088/1126-6708/2001/12/012