Different Traces of Quantum Systems Having the Same Classical Limit

Details Different Traces of Quantum Systems Having the Same Classical Limit Different Traces of Quantum Systems Having the Same Classical Limit

1999-10-29

arxiv.org/abs/chao-dyn/9911001v2

Physica E 9 (2001) 513-517

Nonlinear Sciences

Chaotic Dynamics

LaTeX 4 pages, 2 figures included, final published version

Scientific paper

10.1016/S1386-9477(00)00255-1

Many quantum systems may have the same classical limit. We argue that in the classical limit their traces do not necessarily converge one to another. The trace formula allows to express quantum traces by means of classical quantities as sums over periodic orbits of the classical system. To explain the lack of convergence of the traces we need the quantum corrections to the classical actions of periodic orbits. The four versions of the quantum baker map on the sphere serve as an illustration of this problem.

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