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arXiv · 1607.07211

On the reduced dynamics of a subset of interacting bosonic particles

Manuel Gessner·Andreas Buchleitner
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Abstract

The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an $N$-particle system produces a hierarchical expansion for the subdynamics of $M\leq N$ particles. Truncating this hierarchy with a pure product state ansatz yields the general, nonlinear coherent mean-field equation of motion. In the special case of a contact interaction potential, this reproduces the Gross-Pitaevskii equation. To account for incoherent effects on top of the mean-field evolution, we discuss possible extensions towards a second-order perturbation theory that accounts for interaction-induced decoherence in form of a nonlinear Lindblad-type master equation.

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Manuel Gessner, Andreas Buchleitner. 2016-07-25. On the reduced dynamics of a subset of interacting bosonic particles. https://doi.org/10.1016/j.aop.2018.01.013

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