Non-Hermitian propagation of Hagedorn wavepackets

Caroline Lasser; Roman Schubert; Stephanie Troppmann

doi:10.1063/1.5026043

Non-Hermitian propagation of Hagedorn wavepackets

Caroline Lasser, Roman Schubert, Stephanie Troppmann

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Abstract

We investigate the time evolution of Hagedorn wavepackets by non-Hermitian quadratic Hamiltonians. We state a direct connection between coherent states and Lagrangian frames. For the time evolution, a multivariate polynomial recursion is derived that describes the activation of lower lying excited states, a phenomenon unprecedented for Hermitian propagation. Finally we apply the propagation of excited states to the Davies-Swanson oscillator.

Original language	English
Article number	082102
Journal	Journal of Mathematical Physics
Volume	59
Issue number	8
Early online date	1 Aug 2018
DOIs	https://doi.org/10.1063/1.5026043
Publication status	Published - Aug 2018

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10.1063/1.5026043

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abstract = "We investigate the time evolution of Hagedorn wavepackets by non-Hermitian quadratic Hamiltonians. We state a direct connection between coherent states and Lagrangian frames. For the time evolution, a multivariate polynomial recursion is derived that describes the activation of lower lying excited states, a phenomenon unprecedented for Hermitian propagation. Finally we apply the propagation of excited states to the Davies-Swanson oscillator.",

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AB - We investigate the time evolution of Hagedorn wavepackets by non-Hermitian quadratic Hamiltonians. We state a direct connection between coherent states and Lagrangian frames. For the time evolution, a multivariate polynomial recursion is derived that describes the activation of lower lying excited states, a phenomenon unprecedented for Hermitian propagation. Finally we apply the propagation of excited states to the Davies-Swanson oscillator.

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UR - https://arxiv.org/abs/1507.02858

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