Applications of a metaplectic calculus to Schrödinger evolutions with non-self-adjoint generators | Zendy

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Applications of a metaplectic calculus to Schrödinger evolutions with non-self-adjoint generators

Author(s) -

Joe Viola

Publication year - 2019

Publication title -

journées équations aux dérivées partielles

Language(s) - English

Resource type - Journals

eISSN - 2118-9366

pISSN - 0752-0360

DOI - 10.5802/jedp.671

Subject(s) - symplectic geometry , mathematics , holomorphic function , quadratic equation , calculus (dental) , stochastic calculus , harmonic oscillator , phase space , wave packet , calculus of variations , time scale calculus , quantum stochastic calculus , algebra over a field , pure mathematics , quantum , mathematical analysis , quantum mechanics , physics , multivariable calculus , geometry , quantum dynamics , medicine , stochastic partial differential equation , dentistry , control engineering , engineering , differential equation , quantum process

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.

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