using the eigenvstates of the Harmonic oscillator could we give a meaning to the Hamiltonian
$$ H=\log(a.a^{+}+1) $$
here $ a$ and $ a^{+}$ are the creation/anihilation operators with commutation rules $ [a,a^{+}]=1$ are the energies of the Hamiltonian $$ E_{n}=\log(n+1) $$ for $ n\ge 0$. The idea is that the partition function of this system with discrete energies would be the Riemann zeta function
$$ Z(s)= \sum_{n\ge 0 }e^{-sE_{n}}=\zeta(s)$$ with $ s=1/kt$.