dorsal/arxiv
View SchemaNonlocal looking equations can make nonlinear quantum dynamics local
| Authors | Marek Czachor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9708052 |
| URL | https://arxiv.org/abs/quant-ph/9708052 |
| DOI | 10.1103/PhysRevA.57.4122 |
| Journal | Phys.Rev. A57 (1998) 4122 |
Abstract
A general method for extending a non-dissipative nonlinear Schr\"odinger and Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles is described. It is shown at a general level that the dynamics so obtained is completely separable, which is the strongest condition one can impose on dynamics of composite systems. It requires that for all initial states (entangled or not) a subsystem not only cannot be influenced by any action undertaken by an observer in a separated system (strong separability), but additionally that the self-consistency condition $Tr_2\circ \phi^t_{1+2}=\phi^t_{1}\circ Tr_2$ is fulfilled. It is shown that a correct extension to $N$ particles involves integro-differential equations which, in spite of their nonlocal appearance, make the theory fully local. As a consequence a much larger class of nonlinearities satisfying the complete separability condition is allowed than has been assumed so far. In particular all nonlinearities of the form $F(|\psi(x)|)$ are acceptable. This shows that the locality condition does not single out logarithmic or 1-homeogeneous nonlinearities.
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"abstract": "A general method for extending a non-dissipative nonlinear Schr\\\"odinger and\nLiouville-von Neumann 1-particle dynamics to an arbitrary number of particles\nis described. It is shown at a general level that the dynamics so obtained is\ncompletely separable, which is the strongest condition one can impose on\ndynamics of composite systems. It requires that for all initial states\n(entangled or not) a subsystem not only cannot be influenced by any action\nundertaken by an observer in a separated system (strong separability), but\nadditionally that the self-consistency condition $Tr_2\\circ\n\\phi^t_{1+2}=\\phi^t_{1}\\circ Tr_2$ is fulfilled. It is shown that a correct\nextension to $N$ particles involves integro-differential equations which, in\nspite of their nonlocal appearance, make the theory fully local. As a\nconsequence a much larger class of nonlinearities satisfying the complete\nseparability condition is allowed than has been assumed so far. In particular\nall nonlinearities of the form $F(|\\psi(x)|)$ are acceptable. This shows that\nthe locality condition does not single out logarithmic or 1-homeogeneous\nnonlinearities.",
"arxiv_id": "quant-ph/9708052",
"authors": [
"Marek Czachor"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.57.4122",
"journal_ref": "Phys.Rev. A57 (1998) 4122",
"title": "Nonlocal looking equations can make nonlinear quantum dynamics local",
"url": "https://arxiv.org/abs/quant-ph/9708052"
},
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