Quantum dynamical phase transition in a system with many-body interactions

Details Quantum dynamical phase transition in a system with many-body interactions Quantum dynamical phase transition in a system with many-body interactions

2005-11-27

arxiv.org/abs/cond-mat/0511639v3

Solid State Comm. 141 (2007) 422

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 3 figures, minor changes, fig.2 modified, added references

Scientific paper

10.1016/j.ssc.2006.11.001

We introduce a microscopic Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency $\omega_{0}$. For weak interactions with the environment $1/\tau_{\mathrm{SE}}<2\omega_{0},$ we find a slower oscillation whose amplitude decays with a decoherence rate $1/\tau_{\phi}=1/(2\tau_{\mathrm{SE}% })$. However, beyond a finite critical interaction with the environment, $1/\tau_{\mathrm{SE}}>2\omega_{0}$, the decoherence rate becomes $1/\tau_{\phi}\propto(\omega_{0}^{2})\tau_{\mathrm{SE}}$. The oscillation period diverges showing a \emph{quantum dynamical phase transition}to a Quantum Zeno phase.

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