dorsal/arxiv
View SchemaLocalization and Pattern Formation in Quantum Physics. II. Waveletons in Quantum Ensembles
| Authors | Antonina N. Fedorova, Michael G. Zeitlin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505115 |
| URL | https://arxiv.org/abs/quant-ph/0505115 |
| DOI | 10.1117/12.624111 |
Abstract
In this second part we present a set of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. The key points demonstrating advantages of this approach are: (i) effects of localization of possible quantum states; (ii) effects of non-perturbative multiscales which cannot be calculated by means of perturbation approaches; (iii) effects of formation of complex/collective quantum patterns from localized modes and classification and possible control of the full zoo of quantum states, including (meta) stable localized patterns (waveletons). We demonstrate the appearance of nontrivial localized (meta) stable states/patterns in a number of collective models covered by the (quantum)/(master) hierarchy of Wigner-von Neumann-Moyal-Lindblad equations, which are the result of ``wignerization'' procedure (Weyl-Wigner-Moyal quantization) of classical BBGKY kinetic hierarchy, and present the explicit constructions for exact analytical/numerical computations (fast convergent variational-wavelet representation). Numerical modeling shows the creation of different internal structures from localized modes, which are related to the localized (meta) stable patterns (waveletons), entangled ensembles (with subsequent decoherence) and/or chaotic-like type of behaviour.
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"abstract": "In this second part we present a set of methods, analytical and numerical,\nwhich can describe behaviour in (non) equilibrium ensembles, both classical and\nquantum, especially in the complex systems, where the standard approaches\ncannot be applied. The key points demonstrating advantages of this approach\nare: (i) effects of localization of possible quantum states; (ii) effects of\nnon-perturbative multiscales which cannot be calculated by means of\nperturbation approaches; (iii) effects of formation of complex/collective\nquantum patterns from localized modes and classification and possible control\nof the full zoo of quantum states, including (meta) stable localized patterns\n(waveletons). We demonstrate the appearance of nontrivial localized (meta)\nstable states/patterns in a number of collective models covered by the\n(quantum)/(master) hierarchy of Wigner-von Neumann-Moyal-Lindblad equations,\nwhich are the result of ``wignerization\u0027\u0027 procedure (Weyl-Wigner-Moyal\nquantization) of classical BBGKY kinetic hierarchy, and present the explicit\nconstructions for exact analytical/numerical computations (fast convergent\nvariational-wavelet representation). Numerical modeling shows the creation of\ndifferent internal structures from localized modes, which are related to the\nlocalized (meta) stable patterns (waveletons), entangled ensembles (with\nsubsequent decoherence) and/or chaotic-like type of behaviour.",
"arxiv_id": "quant-ph/0505115",
"authors": [
"Antonina N. Fedorova",
"Michael G. Zeitlin"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"math-ph",
"math.MP",
"nlin.PS"
],
"doi": "10.1117/12.624111",
"title": "Localization and Pattern Formation in Quantum Physics. II. Waveletons in Quantum Ensembles",
"url": "https://arxiv.org/abs/quant-ph/0505115"
},
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