TY - JOUR
T1 - A Central Limit Theorem in Many-Body Quantum Dynamics
AU - Arous, Gérard Ben
AU - Kirkpatrick, Kay
AU - Schlein, Benjamin
N1 - Funding Information:
Benjamin Schlein, Partially supported by an ERC Starting Grant.
Funding Information:
Kirkpatrick, Partially supported by NSF grants OISE-0730136 and DMS-1106770.
PY - 2013/7
Y1 - 2013/7
N2 - We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one step further and we show that the fluctuations around the Hartree evolution satisfy a central limit theorem. Interestingly, the variance of the limiting Gaussian distribution is determined by a time-dependent Bogoliubov transformation describing the dynamics of initial coherent states in a Fock space representation of the system.
AB - We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one step further and we show that the fluctuations around the Hartree evolution satisfy a central limit theorem. Interestingly, the variance of the limiting Gaussian distribution is determined by a time-dependent Bogoliubov transformation describing the dynamics of initial coherent states in a Fock space representation of the system.
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U2 - 10.1007/s00220-013-1722-1
DO - 10.1007/s00220-013-1722-1
M3 - Article
AN - SCOPUS:84878772792
SN - 0010-3616
VL - 321
SP - 371
EP - 417
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -