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We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modelled with unbounded interactions, whence here we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and provide both physically and mathematically motivated examples.
The validity of optimized dynamical decoupling (DD) is extended to analytically time dependent Hamiltonians. As long as an expansion in time is possible the time dependence of the initial Hamiltonian does not affect the efficiency of optimized dynami
It is shown that if the C operator for a PT-symmetric Hamiltonian with simple eigenvalues is not unique, then it is unbounded. Apart from the special cases of finite-matrix Hamiltonians and Hamiltonians generated by differential expressions with PT-s
It is commonly claimed that only Hamiltonians with a spectrum unbounded both above and below can give purely exponential decay. Because such Hamiltonians have no ground state, they are considered unphysical. Here we show that Hamiltonians which are b
The thermal equilibrium properties of physical systems can be described using Gibbs states. It is therefore of great interest to know when such states allow for an easy description. In particular, this is the case if correlations between distant regi
We propose a scheme for mixed dynamical decoupling (MDD), where we combine continuous dynamical decoupling with robust sequences of phased pulses. Specifically, we use two fields for decoupling, where the first continuous driving field creates dresse