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We are at the midst of second quantum revolution where the mesoscopic quantumdevies are actively employed for technological purposes. Despite this fact, thedescription of their real-time dynamics beyond the Fermi's golden rule remainsa formiddable theoretical problem. This is due to the rapid spread ofentanglement within the degrees of freedom of the surrounding environment. Thisis accompanied with a quantum noise (QN) acting on the mesoscopic device. Inthis work we propose a possible way out: to exploit the fact that this QN isusually bandlimited. This is because its spectral density is often contained inpeaks of localized modes and resonances, and may be constrained by bandgaps.Inspired by the Kotelnikov sampling theorem from the theory of classicalbandlimited signals, we put forward and explore the idea that when the QNspectral density has effective bandwidth $B$, the quantum noise becomes adiscrete-time process, with an elementary time step $\tau\propto B^{-1}$. Aftereach time step $\tau$, one new QN degree of freedom (DoF) gets coupled to thedevice for the first time, and one new QN DoF get irreversibly decoupled. Onlya bounded number of QN DoFs are significantly coupled at any time moment. Wecall these DoFs the \textit{Kotelnikov modes}. As a result, the real-timedissipative quantum motion has a natural structure of a discrete-time matrixproduct state, with a bounded bond dimension. This yields a microscopicallyderived collision model. The temporal entanglement entropy appears to bebounded (area-law scaling) in the frame of Kotelnikov modes. The irreversiblydecoupled modes can be traced out as soon as they occur during the real-timeevolution. This leads to a novel\textit{bandlimited} input-output formalism andto quantum jump Monte Carlo simulation techniques for real-time motion of openquantum systems. We illustrate this idea on a spin-boson model.

Beyond The Fermi's Golden Rule: Discrete-Time Decoherence Of Quantum Mesoscopic Devices Due To Bandlimited Quantum Noise