Semiclassical limit of Husimi function

Semiclassical Husimi functions for spin systems

Rigorous derivation of semiclassical approximations in phase space via path integrals [1] for systems with one degree of freedom have recently received considerable attention, both for continuous variables and spin systems. Baranger et al [2], for example, have discussed the canonical coherent state path integral and its semiclassical approximation in some detail, including an initial-value rep...

Spectral Shift Function for Trapping Energies in the Semiclassical Limit

Semiclassical limit and quantum chaos

In this paper we present the field on which R. Rammal was working in the last moments of his life : quantum chaos. The behavior of various distributions is investigated numerically for different planar billiards in presence of a magnetic field or not. We find exponential laws for the distributions of the trajectory lengths, of the algebraic areas, and of the number of boundary reflections. Thes...

The Semiclassical Limit of Loop Quantum Cosmology

The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero–Immirzi parameter γ in controlling space-time discreteness. In this way, standard quantum cosmology is shown to be the simultaneous limit γ → 0, j → ∞ of loop quantum cosmology. Here, j is a label of the volume eigenvalues, and the simultan...

Chaos and semiclassical limit in quantum cosmology.

In this paper we present a Friedmann-Robertson-Walker cosmological model conformally coupled to a massive scalar field where the WKB approximation fails to reproduce the exact solution to the Wheeler-DeWitt equation for large Universes. The breakdown of the WKB approximation follows the same pattern than in semiclassical physics of chaotic systems, and it is associated to the development of sma...