Universität zu Köln

Trimborn, F., Werner, R. F. and Witthaut, D. (2016). Quantum de Finetti theorems and mean-field theory from quantum phase space representations. J. Phys. A-Math. Theor., 49 (13). BRISTOL: IOP PUBLISHING LTD. ISSN 1751-8121

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Trimborn, F. UNSPECIFIED UNSPECIFIED UNSPECIFIED Werner, R. F. UNSPECIFIED UNSPECIFIED UNSPECIFIED Witthaut, D. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-280855
DOI:	10.1088/1751-8113/49/13/135302
Journal or Publication Title:	J. Phys. A-Math. Theor.
Volume:	49
Number:	13
Date:	2016
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1751-8121
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SYMMETRIC STATES; CLASSICAL LIMIT Multiple languages Physics, Multidisciplinary; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/28085