dorsal/arxiv
View SchemaLocalization and Pattern Formation in Quantum Physics. I. Phenomena of Localization
| Authors | Antonina N. Fedorova, Michael G. Zeitlin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505114 |
| URL | https://arxiv.org/abs/quant-ph/0505114 |
| DOI | 10.1117/12.624110 |
Abstract
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i) effects of localization of possible quantum states, more proper than "gaussian-like states"; (ii) effects of non-perturbative multiscales which cannot be calculated by means of perturbation approaches; (iii) effects of formation of complex quantum patterns from localized modes or classification and possible control of the full zoo of quantum states, including (meta) stable localized patterns (waveletons). We'll consider calculations of Wigner functions as the solution of Wigner-Moyal-von Neumann equation(s) corresponding to polynomial Hamiltonians. Modeling demonstrates the appearance of (meta) stable patterns generated by high-localized (coherent) structures or entangled/chaotic behaviour. We can control the type of behaviour on the level of reduced algebraical variational system. At the end we presented the qualitative definition of the Quantum Objects in comparison with their Classical Counterparts, which natural domain of definition is the category of multiscale/multiresolution decompositions according to the action of internal/hidden symmetry of the proper realization of scales of functional spaces. It gives rational natural explanation of such pure quantum effects as ``self-interaction''(self-interference) and instantaneous quantum interaction.
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"abstract": "In these two related parts we present a set of methods, analytical and\nnumerical, which can illuminate the behaviour of quantum system, especially in\nthe complex systems. The key points demonstrating advantages of this approach\nare: (i) effects of localization of possible quantum states, more proper than\n\"gaussian-like states\"; (ii) effects of non-perturbative multiscales which\ncannot be calculated by means of perturbation approaches; (iii) effects of\nformation of complex quantum patterns from localized modes or classification\nand possible control of the full zoo of quantum states, including (meta) stable\nlocalized patterns (waveletons). We\u0027ll consider calculations of Wigner\nfunctions as the solution of Wigner-Moyal-von Neumann equation(s) corresponding\nto polynomial Hamiltonians. Modeling demonstrates the appearance of (meta)\nstable patterns generated by high-localized (coherent) structures or\nentangled/chaotic behaviour. We can control the type of behaviour on the level\nof reduced algebraical variational system. At the end we presented the\nqualitative definition of the Quantum Objects in comparison with their\nClassical Counterparts, which natural domain of definition is the category of\nmultiscale/multiresolution decompositions according to the action of\ninternal/hidden symmetry of the proper realization of scales of functional\nspaces. It gives rational natural explanation of such pure quantum effects as\n``self-interaction\u0027\u0027(self-interference) and instantaneous quantum interaction.",
"arxiv_id": "quant-ph/0505114",
"authors": [
"Antonina N. Fedorova",
"Michael G. Zeitlin"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"math-ph",
"math.MP",
"nlin.PS"
],
"doi": "10.1117/12.624110",
"title": "Localization and Pattern Formation in Quantum Physics. I. Phenomena of Localization",
"url": "https://arxiv.org/abs/quant-ph/0505114"
},
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