4,012 research outputs found

    Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit

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    The many-body localization (MBL) phase transition is not a conventional thermodynamic phase transition. Thus to define the phase transition one should allow the possibility of taking the limit of an infinite system in a way that is not the conventional thermodynamic limit. We explore this for the so-called "avalanche" instability due to rare thermalizing regions in the MBL phase for quenched-random systems in more than one spatial dimension, finding an unconventional way of scaling the systems so that they do have a type of phase transition. These arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension is a transition where entanglement in the eigenstates begins to spread in to some typical regions: the transition is set by when the avalanches start. Once this entanglement gets started, the system does thermalize. From this point of view, the much-studied case of one-dimensional MBL with short-range interactions is a special case with a different, and in some ways more conventional, type of phase transition.Comment: 10 pages, 2 figure

    Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires

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    In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the "spin-incoherent Luttinger liquid'" (SILL) regime] where charge excitations are "cold" (i.e., have low entropy) whereas spin excitations are "hot." We explore the effects of charge-sector disorder in the SILL regime in the absence of external sources of equilibration. We argue that the disorder localizes all charge-sector excitations; however, spin excitations are protected against full localization, and act as a heat bath facilitating charge and energy transport on asymptotically long timescales. The charge, spin, and energy conductivities are widely separated from one another. The dominant carriers of energy are neither charge nor spin excitations, but neutral "phonon" modes, which undergo an unconventional form of hopping transport that we discuss. We comment on the applicability of these ideas to experiments and numerical simulations.Comment: 14 pages, 6 figure

    Convergence rates of the DPG method with reduced test space degree

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    This paper presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree

    Evaluation of Waterhyacinth and Paddy Straw Waste for Culture of Oyster Mushrooms

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    Waterhyacinth ( Eichhornia crassipes (Mart.) Solms.) was evaluated at ratios of 25, 50 and 75% with paddy straw ( Oryza sativa L.) for oyster mushroom ( Pleurotus sajor-caju) cultivation. There was an increase in yield with decreasing ratio waterhyacinth

    Grain orientation in high Tc superconductors by molten salt powder synthesis

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    The molten salt or the flux method is used to fabricate a grain oriented YBa2Cu3O(7-x) (123) superconductor. Here we suggest a two-stage approach in using the 'green phase', Y2BaCuO5 (211), as seed crystals in the formation of YBa2Cu3O(7-x). The process uses Y2BaCuO5 formed by molten salt synthesis. The Y2BaCuO5 phase was observed to be stable in water and in most of the salt systems. Salt processing can form a small quantity of anisotropic particles of Y2BaCuO5. This material can form the 123 phase when tape cast and sintered in the presence of the required levels of Ba and Cu

    Spectral features of a many-body localized system weakly coupled to a heat bath

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    We study many-body-localized (MBL) systems that are weakly coupled to thermalizing environments, focusing on the spectral functions of local operators. We argue that these spectral functions carry signatures of localization even away from the limit of perfectly isolated systems. We find that, in the limit of vanishing coupling to a bath, MBL systems come in two varieties, with either discrete or continuous local spectra. Both varieties of MBL systems exhibit a "soft gap" at zero frequency in the spatially-averaged spectral functions of local operators, which serves as a diagnostic for localization. We estimate the degree to which coupling to a bath broadens these spectral features, and find that characteristics of incipient localization survive as long as the system-bath coupling is much weaker than the characteristic energy scales of the system. Since perfect isolation is impossible, we expect the ideas discussed in this paper to be relevant for all experiments on many-body localization.Comment: Expanded discussion of multiple lengthscales and of properties as a quantum memor

    Weak crystallization theory of metallic alloys

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    We extend the Weak Crystallization theory to the case of metallic alloys. The additional ingredient -- itinerant electrons -- generates nontrivial dependence of free energy on the angles between ordering wave vectors of ionic density. That leads to stabilization of FCC, Rhombohedral, and icosahedral quasicrystalline (iQC) phases, which are absent in the generic theory with only local interactions. The condition for stability of iQC that we find, is consistent with the Hume-Rothery rules known empirically for majority of stable iQC; namely, the length of the primary Bragg peak wavevector is approximately equal to the diameter of the Fermi surface.Comment: 10 pages, 5 figure
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