M. Merkli, G.P. Berman, I.M. Sigal
Dynamics of Collective Decoherence and Thermalization
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ABSTRACT. We analyze the dynamics of $N$ interacting spins (quantum
register) collectively coupled to a thermal environment. Each spin
experiences the same environment interaction, consisting of an
energy conserving and an energy exchange part.
We find the decay rates of the reduced density matrix elements in
the energy basis. We show that if the spins do not interact among each other,
then the fastest decay rates of off-diagonal matrix
elements induced by the energy conserving interaction is of order
$N^2$, while that one induced by the energy exchange interaction
is of the order $N$ only. Moreover, the diagonal matrix
elements approach their limiting values at a rate independent of
$N$.
For a general spin system the decay rates depend
in a rather complicated (but explicit) way on the size $N$ and the interaction between the spins.
Our method is based on a dynamical quantum resonance theory valid
for small, fixed values of the couplings. We do not make Markov-,
Born- or weak coupling (van Hove) approximations.