Details
| Original language | English |
|---|---|
| Article number | 135302 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 49 |
| Issue number | 13 |
| Publication status | Published - 18 Feb 2016 |
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.
Keywords
- BoseEinstein condensate, de Finetti theorem, mean-field theory
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
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In: Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 13, 135302, 18.02.2016.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quantum de Finetti theorems and mean-field theory from quantum phase space representations
AU - Trimborn, F.
AU - Werner, R. F.
AU - Witthaut, D.
PY - 2016/2/18
Y1 - 2016/2/18
N2 - 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.
AB - 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.
KW - BoseEinstein condensate
KW - de Finetti theorem
KW - mean-field theory
UR - http://www.scopus.com/inward/record.url?scp=84960406800&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/49/13/135302
DO - 10.1088/1751-8113/49/13/135302
M3 - Article
AN - SCOPUS:84960406800
VL - 49
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 13
M1 - 135302
ER -