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Soviet Journal of Quantum Electronics

Formation of quantum fields in nonlinear resonators

А. В. Белинский

Published Mar 31, 1991• 0 citations
Publisher

Abstract

Some incorrect statements and conclusions in previous papers by the author are identified. The cause of the error is determined and the scope of valid results in these papers is given. An analysis is made of the conditions of validity of these results and new examples of their use are suggested.
DOI
10.1070/qe1991v021n03abeh003807

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A quantum solution is suggested for the problem of the evolution of a field in a bistable ring resonator containing a nonlinear medium in which phase self-modulation or parametric amplification take place. A broad class of solutions valid for an arbitrary resonator Q factor is derived. It is shown that the known semiclassical descriptions of quantum state preparation in a resonator are inaccurate and in many cases yield incorrect results. For example, optimal suppression of the quantum fluctuations of one of the quadrature components of the field is achieved not at the lasing threshold but below it.
Photons have been shown in this author's prior papers to be spinning, washer shaped, atomic sized particles which are single electric field corpuscles that move orthogonally to the washer face at the local speed of light.Thus, light has no frequency and is not a wave.Perhaps one of the major arguments in favor of light being a wave is that diffraction grating experiments accurately identify the source of the emitted photons.A fundamental assumption in the analysis involving these experiments is that the incident light at the grating slits is a coherent wave.It will be shown in this work that this assumption cannot be valid.However, in spite of this result, and in spite of light being particle shaped and not a wave, it is briefly outlined in this work and shown in an upcoming paper that the conclusions which are drawn concerning source identities are correct.Thus, these spectroscopy experiments have great value even though the wavelengths they indicate do not exist.
Abstract. In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under strong dissipative conditions, numerous previous works have established rigorous error bounds and linear convergence for Carleman linearization, which have facilitated the identification of quantum advantages in simulating large-scale dynamical systems. Our analysis extends these findings by exploring error bounds beyond the traditional dissipative condition, thereby broadening the scope of quantum computational benefits to a new class of dynamical regimes. This novel regime is defined by a resonance condition, and we prove how this resonance condition leads to a linear convergence with respect to the truncation level [Formula: see text] in Carleman linearization. We support our theoretical advancements with numerical experiments on a variety of models, including the Burgers’ equation, Fermi–Pasta–Ulam (FPU) chains, and the Korteweg-de Vries (KdV) equations, to validate our analysis and demonstrate the practical implications.