# What is behind recoherence?

I am quite familiar with the concept of decoherence, and I heard that a system that has decohered could recohere after that, I was wondering what could cause the the coherences that have leaked into the environment to come back to the system. I heard about thermal fluctuations for example, without being able to understand this argument.

Thanks.

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If you consider the thermal fluctuations that arise from coupling the system to a heat bath, then if the dynamics of the open system is non-Markovian then you can have recoherence and if the dynamics of the open system is Markovian (Lindblad master equation) then you will only have decoherence.

Non-Markovian means that there are non-vanishing timescales associated with the bath dynamics, relative to the system. The environment is said to have memory. The dynamics of the system at a particular time is not only a function of the state of the system at that time, but also its past history of states. In this way, recoherence will only occur if there has been sufficient decoherence in the past. Anti-dissipation (amplification) and anti-diffusion is also possible, both quantum mechanically and in classical open systems.

A simpler example would be to consider a small quantum system with two degrees of freedom coupled together and trace out one degree of freedom. In many cases the remaining open system would experience an endless cycle of decoherence and recoherence.

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The bold and brilliant pioneer Susskind came up with the causal patch conjecture. The universe is accelerating and will approach de Sitter space. The universe right up to the cosmological horizon is all that exists. Nothing beyond exists. The Hilbert space of the universe is finite in dimensionality, approximately $e^{10^{123}}$ in size. A classical system this size will undergo Poincare recurrence at a timescale of the order of the number of states, but a quantum system with wave function components which can interfere will undergo a recurrence in about $\exp\{e^{10^{123}}\}$. Recoherence will happen by then. You can read up more about it in the brilliant conversations between Simplicio, Sagredo and Salviati at The Multiverse Interpretation of Quantum Mechanics. Check out their discussion on "unhappening".