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We investigate the possibility to control localization properties of the asymptotic state of an open quantum system with a tunable synthetic dissipation. The control mechanism relies on the matching between properties of dissipative operators, acting on neighboring sites and specified by a single control parameter, and the spatial phase structure of eigenstates of the system Hamiltonian. As a result, the latter coincide (or near coincide) with the dark states of the operators. In a disorder-free Hamiltonian with a flat band, one can either obtain a localized asymptotic state or populate whole flat and/or dispersive bands, depending on the value of the control parameter. In a disordered Anderson system, the asymptotic state can be localized anywhere in the spectrum of the Hamiltonian. The dissipative control is robust with respect to an additional local dephasing.
Many-body localization (MBL) is a result of the balance between interference-based Anderson localization and many-body interactions in an ultra-high dimensional Fock space. It is usually expected that dissipation is blurring interference and destroyi
Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry
The robustness of quantum control in the presence of uncertainties is important for practical applications but their quantum nature poses many challenges for traditional robust control. In addition to uncertainties in the system and control Hamiltoni
Ergodicity in quantum many-body systems is - despite its fundamental importance - still an open problem. Many-body localization provides a general framework for quantum ergodicity, and may therefore offer important insights. However, the characteriza
The Anderson delocalization-localization transition is studied in multilayered systems with randomly placed interlayer bonds of density $p$ and strength $t$. In the absence of diagonal disorder (W=0), following an appropriate perturbation expansion,