Local scaling asymptotics for the Gutzwiller trace formula in Berezin-Toeplitz quantization (Q1651380)

This paper is concerned with semiclassical aspects of the Berezin-Toeplitz quantization of a Kähler manifold \((M, J, 2\omega )\). The Gutzwiller trace formula deals with the asymptotics of the trace of the distributional kernel of a smoothed spectral projector relative to a spectral band of width \(O(\hbar )\) around an energy value. The autor studies a Gutzwiller-Toeplitz kernel from the point of view of asymptotically concentration along appropriate classical loci defined by the dynamics, with an explicit description of the exponential decay in normal directions.