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An integrable Hamiltonian system presents monodromy if the action-angle variables cannot be defined globally. We consider a classical system with azimuthal symmetry and explore the topology structure of its phase space. Based on the behavior of closed orbits around singular points or regions of the energy-momentum plane, a semi-theoretical method is derived to detect classical monodromy. The validity of the monodromy test is numerically illustrated for several systems with azimuthal symmetry.
In this article we discuss our ongoing program to extend the scope of certain, well-developed microlocal methods for the asymptotic solution of Schr{o}dingers equation (for suitable `nonlinear oscillatory quantum mechanical systems) to the treatment
We develop physically admissible lattice models in the harmonic approximation which define by Hamiltons variational principle fractional Laplacian matrices of the forms of power law matrix functions on the n -dimensional periodic and infinite lattice
We consider the quantum evolution $e^{-ifrac{t}{hbar}H_{beta}} psi_{xi}^{hbar}$ of a Gaussian coherent state $psi_{xi}^{hbar}in L^{2}(mathbb{R})$ localized close to the classical state $xi equiv (q,p) in mathbb{R}^{2}$, where $H_{beta}$ denotes a sel
Expository paper on the relations between perturbation theory of pseudo-differential operators, finiteness theorems and deformations of Lagrangian varieties.
in the recent paper [Journal of Physics A, 43474-0288 (2011)], B. Helffer and R. Purice compute the second term of a semi-classical trace formula for a Schrodinger operator with magnetic field. We show how to recover their formula by using the method