The Fourier method

Komech, Alexander; Komech, Alexander

doi:10.1007/978-1-4419-1096-7_2

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2011

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“…Such seems also the case for the quantum properties related to non-orthogonality between the one-particle mean-field nonlinear eigenstates. Therefore any attempt to investigate the time-dependent relationship between linear and nonlinear eigenstates of a given quantum system -like the recent attempt to both display particular nonlinear eigenfunctions as global attractors for all finite-energy solutions and describe quantum transitions between them [28]-are welcome. However, only a comparison with experiments and the solutions of the original linear manyparticle problem can shed a definite light on these questions.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear interference in a mean-field quantum model

Reinisch

Guðmundsson

2011

Eur. Phys. J. B

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Using similar nonlinear stationary mean-field models for Bose-Einstein Condensation of cold atoms and interacting electrons in a Quantum Dot, we propose to describe the original many-particle ground state as a one-particle statistical mixed state of the nonlinear eigenstates whose weights are provided by the eigenstate non-orthogonality. We search for physical grounds in the interpretation of our two main results, namely, quantum-classical nonlinear transition and interference between nonlinear eigenstates. PACS numbers: 73.21.La 71.10.Li 71.90+q arXiv:1007.2408v1 [cond-mat.mes-hall]

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Section: Discussionmentioning

confidence: 99%