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- W2945806987 abstract "We study the Bose and Fermi Hubbard model in the (formal) limit of large coordination numbers $Zgg1$. Via an expansion into powers of $1/Z$, we establish a hierarchy of correlations which facilitates an approximate analytical derivation of the time-evolution of the reduced density matrices for one and two sites etc. With this method, we study the quantum dynamics (starting in the ground state) after a quantum quench, i.e., after suddenly switching the tunneling rate $J$ from zero to a finite value, which is still in the Mott regime. We find that the reduced density matrices approach a (quasi) equilibrium state after some time. For one lattice site, this state can be described by a thermal state (within the accuracy of our approximation). However, the (quasi) equilibrium state of the reduced density matrices for two sites including the correlations cannot be described by a thermal state. Thus, real thermalization (if it occurs) should take much longer time. This behavior has already been observed in other scenarios and is sometimes called ``pre-thermalization.'' Finally, we compare our results to numerical simulations for finite lattices in one and two dimensions and find qualitative agreement." @default.
- W2945806987 created "2019-05-29" @default.
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- W2945806987 date "2013-11-09" @default.
- W2945806987 modified "2023-09-27" @default.
- W2945806987 title "Equilibration versus (pre) thermalization in the Bose and Fermi Hubbard models" @default.
- W2945806987 hasPublicationYear "2013" @default.
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