After a quantum quench, a sudden change of parameters, generic many particle quantum systems are expected to equilibrate. A few collisions of quasiparticles are usually sufficient to establish approximately local equilibrium. Reaching global equilibrium is, however, much more difficult as conserved quantities have to be transported for long distances to build up a pattern of fluctuations characteristic for equilibrium. Here we investigate the quantum quench of the one-dimensional bosonic Hubbard model from infinite to finite interaction strength U using semiclassical methods for weak, and exact diagonalization for strong quenches. Equilibrium is approached only slowly, as t^{-1/2} with subleading corrections proportional to t^{-3/4}, consistent with predictions from hydrodynamics. We show that these long-time tails determine the relaxation of a wide range of physical observables.Comment: 5 pages + 4 pages Supplementary Materia

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With the recent discovery of Weyl semimetals, the phenomenon of negative magnetoresistance (MR) is attracting renewed interest. Large negative MR is usually related to magnetism, but the chiral anomaly in Weyl semimetals is a rare exception. Here we report a mechanism for large negative MR which is also unrelated to magnetism but is related to disorder. In the nearly bulk-insulating topological insulator TlBi0.15Sb0.85Te2, we observed gigantic negative MR reaching 98% in 14 T at 10 K, which is unprecedented in a nonmagnetic system. Supported by numerical simulations, we argue that this phenomenon is likely due to the Zeeman effect on a barely percolating current path formed in the disordered bulk. Since disorder can also lead to non-saturating linear MR in Ag2+δSe, the present finding suggests that disorder engineering in narrow-gap systems is useful for realizing gigantic MR in both positive and negative directions.

The topological insulator BiSbTeSe2 corresponds to a compensated semiconductor in which strong Coulomb disorder gives rise to the formation of charge puddles, i.e., local accumulations of charge carriers, both in the bulk and on the surface. Bulk puddles are formed if the fluctuations of the Coulomb potential are as large as half of the band gap. The gapless surface, in contrast, is sensitive to small fluctuations but the potential is strongly suppressed due to the additional screening channel provided by metallic surface carriers. To study the quantitative relationship between the properties of bulk puddles and surface puddles, we performed infrared transmittance measurements as well as scanning tunneling microscopy measurements on the same sample of BiSbTeSe2, which is close to perfect compensation. At 5.5 K, we find surface potential fluctuations occurring on a length scale rs = 40 − 50 nm with amplitude Γ = 8 − 14 meV which is much smaller than in the bulk, where optical measurements detect the formation of bulk puddles. In this nominally undoped compound, the value of Γ is smaller than expected for pure screening by surface carriers, and we argue that this arises most likely from a cooperative effect of bulk screening and surface screening. arXiv:1708.09166v1 [cond-mat.mes-hall]

The linear fractional map f (z) = az+b cz+d on the Riemann sphere with complex coefficients ad − bc = 0 is called Möbius map. If f satisfies ad − bc = 1 and −2 < a + d < 2, then f is called elliptic Möbius map. Let {b n } n∈N 0 be the solution of the elliptic Möbius difference equation b n+1 = f (b n ) for every n ∈ N 0 . Then the sequence {b n } n∈N 0 has no Hyers-Ulam stability.