= Zurek spin-bath model
{c}
{title2=$H=-Z_D\otimes\sum_k g_kZ_k$}
A device qubit couples diagonally to a finite bath of spins. Conditional bath states acquire opposite phase rotations, and their <conditional environment overlap> multiplies the device coherence. An initially aligned bath leaves the overlap's modulus at one. Initially equatorial spins yield $z_N(t)=\prod_k\cos(2g_kt)$. Global <unitary time evolution> remains reversible, and a <finite spin-bath coherence recurrence> prevents a strict zero long-time limit at finite bath size.
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