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One-Parameter Gaussian State of Anharmonic Oscillator: Nonlinear Realization of Bogoliubov Transformation

Jung Kon Kim·Sang Pyo Kim·Kwang-Gi Park
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Abstract

We find a one-parameter Gaussian state for an anharmonic oscillator with quadratic and quartic terms, which depends on the energy expectation value. For the weak coupling constant, the Gaussian state is a squeezed state of the vacuum state. However, for the strong coupling constant, the Gaussian state represents a different kind of condensation of bosonic particles through a nonlinear Bogoliubov transformation of the vacuum state.

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Jung Kon Kim, Sang Pyo Kim, Kwang-Gi Park. 1999-02-11. One-Parameter Gaussian State of Anharmonic Oscillator: Nonlinear Realization of Bogoliubov Transformation. https://arxiv.org/abs/quant-ph/9902047

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