Is interaction a relevant perturbation for 1d Anderson localization of fermions?
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I have read that weak localization is a precursor to Anderson localization. Weak localization happens due to the constructive interference between paths that loop around in opposite direction, on account of guaranteed identity of phases accumulated in time reversed paths. This leads to a slightly higher than expected probability for the particle to stay back as opposed to move to a different location.
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Hey dear here is the answer
One-dimensional bosons in disorder provide a perfect system for studying a generic phenomenon of many-body localization–delocalization transition. After the observation of single-particle Anderson localization in dilute clouds of bosonic atoms, the obvious direction of research is to describe the effects of repulsion between the bosons. Theoretical studies of 1D interacting bosons have a long history. In the case of strong enough repulsion and zero temperature, the problem was solved by Giamarchi and Schulz in 1988, and, more recently, the limit of weak repulsion was analyzed. However, the full picture of finite temperature and arbitrary interaction strength has remained an open problem. In this paper, we develop such a theory and establish predictions that can be confronted to experiment.
Hope its help you
One-dimensional bosons in disorder provide a perfect system for studying a generic phenomenon of many-body localization–delocalization transition. After the observation of single-particle Anderson localization in dilute clouds of bosonic atoms, the obvious direction of research is to describe the effects of repulsion between the bosons. Theoretical studies of 1D interacting bosons have a long history. In the case of strong enough repulsion and zero temperature, the problem was solved by Giamarchi and Schulz in 1988, and, more recently, the limit of weak repulsion was analyzed. However, the full picture of finite temperature and arbitrary interaction strength has remained an open problem. In this paper, we develop such a theory and establish predictions that can be confronted to experiment.
Hope its help you
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