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《Physics letters. A》2020,384(7):126152
Derived from quantum waves immersed in an Abelian gauge potential, the quasiperiodic Aubry-André-Harper (AAH) model is a simple yet powerful Hamiltonian to study the Anderson localization of ultracold atoms. Here, we investigate the localization properties of ultracold atoms in quasiperiodic optical lattices subject to a non-Abelian gauge potential, which are depicted by non-Abelian AAH models. We identify that the non-Abelian AAH models can bear the self-duality. We analyze the localization of such non-Abelian self-dual optical lattices, revealing a rich phase diagram driven by the non-Abelian gauge potential involved: a transition from a pure delocalization phase, then to coexistence phases, and finally to a pure localization phase. This is in stark contrast to the Abelian counterpart that does not support the coexistence phases. Our results establish the connection between localization and gauge symmetry, and thus comprise a new insight on the fundamental aspects of localization in quasiperiodic systems, from the perspective of non-Abelian gauge potential. 相似文献
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《Mathematische Nachrichten》2017,290(10):1544-1552
Let K and S be locally compact Hausdorff spaces and X be an abstract space. Suppose that T is a positive Banach lattice isomorphism from into . Then for each ordinal α the cardinalities of the αth derivatives and satisfy the following inequality Moreover, if then is a continuous image of a subset of which can be taken closed when K is compact. The first statement of this result for is a vector‐valued extension of a Cengiz's theorem and the second one is vector‐valued version of a Holsztyński's theorem. A simple example shows that the number is sharp in these vector‐valued theorems. 相似文献
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Francesco dellIsola Emilio Turco Anil Misra Zacharias Vangelatos Costas Grigoropoulos Vasileia Melissinaki Maria Farsari 《Comptes Rendus Mecanique》2019,347(5):397-405
In this paper, we reveal that the mathematical discrete model of Hencky type, introduced in [1], is appropriate for describing the mechanical behavior of micro-metric pantographic elementary modules. This behavior does not differ remarkably from what has been observed for milli-metric modules, as we prove with suitably designed experiments. Therefore, we conclude that the concept of pantographic microstructure seems feasible for micro-metrically architected microstructured (meta)materials as well. These results are particularly indicative of the possibility of fabricating materials that can have an underlying pantographic microstructure at micrometric scale, so that its unique behavior can be exploited in a larger range of technological applications. 相似文献
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A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper
to simulate spatiotemporal chaos in fluid flows. It is found that the parameter region of spatiotemporal chaos can be determined
by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for
turbulence such that the route to spatiotemporal chaos in fluid flows can be envisaged.
The study is supported by “Nonlinear Sciences Project” from the State Science and Technology Commission of China. 相似文献
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Relations Between Relaxation Modulus and Creep Compliance in Anisotropic Linear Viscoelasticity 总被引:2,自引:0,他引:2
The results obtained previously for scalar and class P completely monotone relaxation moduli are extended to arbitrary anisotropy.
It is shown for general anisotropic viscoelastic media that, if the relaxation modulus is a locally integrable completely
monotone function, then the creep compliance is a Bernstein function and conversely. The elastic and equilibrium limits of
the two material functions are related to each other. The relaxation modulus or its derivative can be singular at 0. A rigorous
general formulation of the relaxation spectrum in an anisotropic viscoelastic medium is given. The effect of Newtonian viscosity
on creep compliance is examined.
Put some makeup on him and lay him to rest. Anonymous 相似文献