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  Quantum de Finetti theorems and mean-field theory from quantum phase space representations.

Trimborn, F., Werner, R. F., & Witthaut, D. (2016). Quantum de Finetti theorems and mean-field theory from quantum phase space representations. Journal of Physics A: Mathematical and Theoretical, 49(13): 135302. doi:10.1088/1751-8113/49/13/135302.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-3B28-A Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-34F5-F
Genre: Journal Article

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 Creators:
Trimborn, F., Author
Werner, R. F., Author
Witthaut, Dirk1, Author              
Affiliations:
1Max Planck Research Group Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063295              

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Free keywords: Mean-field theory; De Finetti theorem; Bose–Einstein condensate
 Abstract: We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose–Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross–Pitaevskii equation.

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Language(s): eng - English
 Dates: 2016-02-182016-04-01
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1088/1751-8113/49/13/135302
 Degree: -

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Title: Journal of Physics A: Mathematical and Theoretical
Source Genre: Journal
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Publ. Info: -
Pages: 28 Volume / Issue: 49 (13) Sequence Number: 135302 Start / End Page: - Identifier: -