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Open Quantum Systems Decoherence

A novel hierarchy of two-family-parameter equations: Local, nonlocal, and mixed-local-nonlocal vector nonlinear Schrodinger equations

arXiv

Authors: Zhenya Yan

Year

2017

Paper ID

24918

Status

Preprint

Abstract Read

~2 min

Abstract Words

184

Citations

N/A

Abstract

We use two families of parameters \{$ε_{x_j}, ε_{t_j}$ | ε_{x_j,t_j}=pm1, j=1,2,...,n\} to first introduce a unified novel two-family-parameter system simply called ${mathcal Q}^{(n}_{ε_{x_{\vec{n}}},ε_{t_{\vec{n}}}}system), connecting integrable local, nonlocal, novel mixed-local-nonlocal, and other nonlocal vector nonlinear Schrödinger (VNLS) equations. The{\mathcal Q}^{(n)}_{ε_{x_{\vec{n}}}, ε_{t_{\vec{n}}}}system withε_{x_j}, ε_{t_j}=pm 1, 1,\, j=1,2,...,nis shown to possess Lax pairs and infinite number of conservation laws. Moreover, we also analyze the{\mathcal PT}symmetry of the Hamiltonians with self-induced potentials. The multi-linear forms and some symmetry reductions are also studied. In fact, the used two families of parameters can also be extended to the general case\{ε_{x_j}, ε_{t_j} | ε_{x_j} = e^{iθ_{x_j}}, ε_{t_j} = e^{iθ_{t_j}},\, θ_{x_j}, θ_{t_j}\in [0, 2π),\, j=1,2,...,n\}$ to generate more types of nonlinear equations. The two-family-parameter idea used in this paper can also be applied to other local nonlinear evolution equations such that novel integrable and non-integrable nonlocal and mixed-local-nonlocal systems can also be found.

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We use two families of parameters (εxj, εtj) | εxj,tj=pm1, j=1,2,...,n to first introduce a unified novel two-family-parameter system simply called mathcal...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1711.09222 [2] arXiv https://arxiv.org/abs/1711.09222 [3] Publisher https://arxiv.org/abs/1711.09222

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