Quantum half-planes via deformation quantization.

Do Ngoc Diep; Nguyen Viet Hai

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Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula

Frédéric Faure (2007)

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We consider a nonlinear area preserving Anosov map $M$ on the torus phase space, which is the simplest example of a fully chaotic dynamics. We are interested in the quantum dynamics for long time, generated by the unitary quantum propagator $\hat{M}$ . The usual semi-classical Trace formula expresses $T r ({\hat{M}}^{t})$ for finite time $t$ , in the limit $ℏ \to 0$ , in terms of periodic orbits of $M$ of period $t$ . Recent work reach time $t ≪ t_{E} / 6$ where $t_{E} = log (1 / ℏ) / λ$ is the Ehrenfest time, and $λ$ is the Lyapounov coefficient. Using a semi-classical...

Self-consistent-field method and $τ$ -functional method on group manifold in soliton theory: a review and new results.

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A $q$ -analogue of the centralizer construction and skew representations of the quantum affine algebra.

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