Results 1 - 10 of 21710
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[en] Local symmetries are spatial symmetries present in a subdomain of a complex system. By using and extending a framework of so-called non-local currents that has been established recently, we show that one can gain knowledge about the structure of eigenstates in locally symmetric setups through a Kirchhoff-type law for the non-local currents. The framework is applicable to all discrete planar Schrödinger setups, including those with non-uniform connectivity. Conditions for spatially constant non-local currents are derived and we explore two types of locally symmetric subsystems in detail, closed-loops and one-dimensional open ended chains. We find these systems to support locally similar or even locally symmetric eigenstates. - Highlights: • We extend the framework of non-local currents to discrete planar systems. • Structural information about the eigenstates is gained. • Conditions for the constancy of non-local currents are derived. • We use the framework to design two types of example systems featuring locally symmetric eigenstates.
[en] We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one-dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non-integer N and for 3D Laplacian problems. (fast track communication)
[en] In the one-dimensional case, for a function satisfying the Gurov-Reshetnyak condition, the infimum of the indices of the Muckenhoupt classes containing this function is found. It is also shown that each Muckenhoupt class lies in some Gurov-Reshetnyak class
[en] The three-spectral inverse problem for a Stieltjes string (a thread bearing finite number of point masses) is solved. The inverse problem for a Stieltjes string damped at an interior point with the ends fixed appears to be closely connected to the corresponding three-spectral problem. Conditions obtained are necessary and sufficient for a set of complex numbers to be the spectrum of a Stieltjes string damped at an interior point
[en] We provide a necessary and sufficient condition under which the quenched central limit theorem without random centering holds for one-dimensional random systems that are uniformly expanding. This condition holds in particular when all the maps preserve a common measure. We also give a counter example which shows that this condition is not necessarily satisfied when the maps do not preserve a common measure. (paper)
[en] A method is presented for the implementation of edge local complementation (ELC) in graph states, based on the application of two Hadamard operations and a single controlled-phase (CZ) gate. As an application, we demonstrate an efficient scheme for constructing a one-dimensional logical cluster state based on the five-qubit quantum error-correcting code, using a sequence of ELCs. A single physical CZ operation, together with local operations, is sufficient to create a logical CZ operation between two logical qubits. This approach in concatenation may allow one to create a hierarchical quantum network for quantum information tasks.
[en] In this paper a new one-dimensional discrete chaotic map based on the composition of permutations is presented. Proposed map is defined over finite set and represents fully digital approach which is significantly different from previous ones. Dynamical properties of special case of proposed map are analyzed. Analyzed map does not have fixed points and exhibits chaotic behavior
[en] We consider methods for estimating one-dimensional oscillatory integrals with convex phase and amplitudes of bounded variation or Lipschitz class amplitudes. In particular, we improve the estimate for the Piercey integral with near-caustic parameter values, and also consider estimation methods for n-dimensional oscillatory integrals