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Open Quantum Systems Decoherence Quantum Simulation

A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting

arXiv

Authors: Javier de Lucas, Julia Lange, Xavier Rivas

Year

2023

Paper ID

53482

Status

Preprint

Abstract Read

~2 min

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Abstract

By using the theory of analytic vectors and manifolds modelled on normed spaces, we provide a rigorous symplectic differential geometric approach to t-dependent Schrödinger equations on separable (possibly infinite-dimensional) Hilbert spaces determined by unbounded t-dependent self-adjoint Hamiltonians satisfying a technical condition. As an application, the Marsden--Weinstein reduction procedure is employed to map above-mentioned t-dependent Schrödinger equations onto their projective spaces. Other applications of physical and mathematical relevance are also analysed.

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By using the theory of analytic vectors and manifolds modelled on normed spaces, we provide a rigorous symplectic differential geometric approach to t-dependent Schrödinger...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2312.09192 [2] arXiv https://arxiv.org/abs/2312.09192 [3] Publisher https://arxiv.org/abs/2312.09192

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