Applications of a metaplectic calculus to Schrödinger evolutions with non-self-adjoint generators
Viola, Joe1
1 Université de Nantes Nantes France
Journées équations aux dérivées partielles (2018), Exposé no. 11, 11 p.

We review the calculus of metaplectic operators and shifts in phase space applied to Gaussian wave packets. Using holomorphic extensions of this calculus, one can reduce the L2 theory of evolution equations with non-selfadjoint quadratic generators to symplectic linear algebra. We illustrate these methods through an application to the quantum harmonic oscillator with complex perturbation ix.

Publié le :
DOI : 10.5802/jedp.671
Viola, Joe 1

1 Université de Nantes Nantes France 
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Viola, Joe. Applications of a metaplectic calculus to Schrödinger evolutions with non-self-adjoint generators. Journées équations aux dérivées partielles (2018), Exposé no. 11, 11 p. doi : 10.5802/jedp.671. https://www.numdam.org/articles/10.5802/jedp.671/

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[12] Said, Mona Ben; Nier, Francis; Viola, Joe Quaternionic structure and analysis of some Kramers-Fokker-Planck operators (2018) (https://arxiv.org/abs/1807.01881)

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[16] Viola, Joe The norm of the non-self-adjoint harmonic oscillator semigroup, Integral Equations Oper. Theory, Volume 85 (2016) no. 4, pp. 513-538

[17] Viola, Joe The elliptic evolution of non-self-adjoint degree-2 Hamiltonians (2017) (https://arxiv.org/abs/1701.00801)

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