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Sandro Graffi

  1. Convergence of a quantum normal form and an exact quantization formula.

    Пнд, 02/07/2011 - 16:01 — SomNambul
    Authors: Sandro Graffi, Thierry Paul
    Subjects: Dynamical Systems
    Abstract

    We consider the Schr\"odinger operator defined by the quantization of the
    linear flow of diophantine frequencies over the l-dimensional torus, perturbed
    by a holomorphic potential which depends on the actions only through their
    particular linear combination defining the Hamiltonian of the linear flow.

  2. Geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schr\"odinger propagator.

    Чт, 06/10/2010 - 15:01 — SomNambul
    Authors: Sandro Graffi, Lorenzo Zanelli
    Subjects: Mathematical Physics
    Abstract

    We construct a family of Fourier Integral Operators, defined for arbitrary
    large times, representing a global parametrix for the Schr\"odinger propagator
    when the potential is quadratic at infinity. This construction is based on the
    geometric approach to the corresponding Hamilton-Jacobi equation and thus
    sidesteps the problem of the caustics generated by the classical flow.
    Moreover, a detailed study of the real phase function allows us to recover a
    WKB semiclassical approximation which necessarily involves the multivaluedness
    of the graph of the Hamiltonian flow past the caustics.

  3. PT Symmetric Schr\"odinger Operators: Reality of the Perturbed Eigenvalues.

    Чт, 01/21/2010 - 16:01 — SomNambul
    Authors: Francesco Cannata, Emanuela Caliceti, Sandro Graffi
    Subjects: Mathematical Physics
    Abstract

    We prove the reality of the perturbed eigenvalues of some PT symmetric
    Hamiltonians of physical interest by means of stability methods. In particular
    we study 2-dimensional generalized harmonic oscillators with polynomial
    perturbation and the one-dimensional $x^2(ix)^{\epsilon}$ for $-1<\epsilon<0$.

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