Intrinsic Origin of 1/f Noise in Open Quantum Systems

1/f noise pollutes open quantum systems. The equilibrium noise power spectrum approaches zero as the frequency and temperature approach zero in the standard approach. This is the same requirement that the Hamiltonian of the system be lower bound. As a result, the standard approach is unable to account for 1/f noise without surrendering the lower bound on energy. In this work, we simplified and optimized the exact fourth-order generator of dynamics in open quantum systems. For the first time, formal 1/f noise terms appear in the master equation in open quantum systems with bounded Hamiltonians. We show that 1/f noise results from the asymptotic incompleteness of Fock space, which can happen when the Hamiltonian does not admit a ground state. It arises when infinitely many bosons are emitted into the environment while the system relaxes. The fourth-order generator allows simultaneous emissions of two bosons into the environment. One boson is at the system Bohr frequency, and the other is at zero frequency, which displaces the bath. The number of zero-frequency bosons can diverge when time goes to infinity. Long-range entanglement develops, and the small quantum system exhibits divergent dynamics. We demonstrate how the asymptotic incompleteness might account not only for 1/f noise, but also for the quantum coherences observed in the quantum biological Fenna-Matthews-Olson complex.