dorsal/arxiv
View SchemaFidelity and Purity Decay in Weakly Coupled Composite Systems
| Authors | Marko Znidaric, Tomaz Prosen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209145 |
| URL | https://arxiv.org/abs/quant-ph/0209145 |
| DOI | 10.1088/0305-4470/36/10/307 |
| Journal | J.Phys.A 36 2463-81 (2003) |
Abstract
We study the stability of unitary quantum dynamics of composite systems (for example: central system + environment) with respect to weak interaction between the two parts. Unified theoretical formalism is applied to study different physical situations: (i) coherence of a forward evolution as measured by purity of the reduced density matrix, (ii) stability of time evolution with respect to small coupling between subsystems, and (iii) Loschmidt echo measuring dynamical irreversibility. Stability has been measured either by fidelity of pure states of a composite system, or by the so-called reduced fidelity of reduced density matrices within a subsystem. Rigorous inequality among fidelity, reduced-fidelity and purity is proved and a linear response theory is developed expressing these three quantities in terms of time correlation functions of the generator of interaction. The qualitatively different cases of regular (integrable) or mixing (chaotic in the classical limit) dynamics in each of the subsystems are discussed in detail. Theoretical results are demonstrated and confirmed in a numerical example of two coupled kicked tops.
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"abstract": "We study the stability of unitary quantum dynamics of composite systems (for\nexample: central system + environment) with respect to weak interaction between\nthe two parts. Unified theoretical formalism is applied to study different\nphysical situations: (i) coherence of a forward evolution as measured by purity\nof the reduced density matrix, (ii) stability of time evolution with respect to\nsmall coupling between subsystems, and (iii) Loschmidt echo measuring dynamical\nirreversibility. Stability has been measured either by fidelity of pure states\nof a composite system, or by the so-called reduced fidelity of reduced density\nmatrices within a subsystem. Rigorous inequality among fidelity,\nreduced-fidelity and purity is proved and a linear response theory is developed\nexpressing these three quantities in terms of time correlation functions of the\ngenerator of interaction. The qualitatively different cases of regular\n(integrable) or mixing (chaotic in the classical limit) dynamics in each of the\nsubsystems are discussed in detail. Theoretical results are demonstrated and\nconfirmed in a numerical example of two coupled kicked tops.",
"arxiv_id": "quant-ph/0209145",
"authors": [
"Marko Znidaric",
"Tomaz Prosen"
],
"categories": [
"quant-ph",
"nlin.CD"
],
"doi": "10.1088/0305-4470/36/10/307",
"journal_ref": "J.Phys.A 36 2463-81 (2003)",
"title": "Fidelity and Purity Decay in Weakly Coupled Composite Systems",
"url": "https://arxiv.org/abs/quant-ph/0209145"
},
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