= Spin-boson model
A spin-boson model couples a two-state <quantum system> to a collection of <quantum harmonic oscillators>. The oscillator modes provide environmental degrees of freedom that can exchange energy with the <spin> and change its <reduced density matrix>. One transverse-coupling convention is
$$
H=\frac{\hbar\Omega}2\sigma_z+\sum_j\hbar\omega_j(a_j^\dagger a_j+1/2)
+\sigma_x\sum_j\lambda_j(a_j^\dagger+a_j).
$$
The choice of coupling axis matters: here the <Pauli matrix> $\sigma_x$ flips the energy-basis <spin> states. Coupling only through $\sigma_z$ has a different effect, since it commutes with the free spin <Hamiltonian operator>.
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