268,489 research outputs found

    Once again: Instanton method vs. WKB

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    A recent analytic test of the instanton method performed by comparing the exact spectrum of the LameËŠ{\acute e} potential (derived from representations of a finite dimensional matrix expressed in terms of su(2)su(2) generators) with the results of the tight--binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the LameËŠ{\acute e} potential as well as others the WKB--related method of matched asymptotic expansions yields the exact instanton result as a result of boundary conditions imposed on wave functions which are matched in domains of overlap.Comment: 10 pages, no figures. References list revised according to JHE

    A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity

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    In the first part of this work, we analyzed a Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D polygonal domain, we also proved an optimal superlinear convergence rate for the control under certain assumptions on the domain and on the target state. In this work, we revisit the convergence analysis without these assumptions; in this case, the solution can have low regularity and we use a different analysis approach. We again prove an optimal convergence rate for the control, and present numerical results to illustrate the convergence theory

    Octupole degree of freedom for the critical-point candidate nucleus 152^{152}Sm in a reflection-asymmetric relativistic mean-field approach

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    The potential energy surfaces of even-even 146−156^{146-156}Sm are investigated in the constrained reflection-asymmetric relativistic mean-field approach with parameter set PK1. It is shown that the critical-point candidate nucleus 152^{152}Sm marks the shape/phase transition not only from U(5) to SU(3) symmetry, but also from the octupole-deformed ground state in 150^{150}Sm to the quadrupole-deformed ground state in 154^{154}Sm. By including the octupole degree of freedom, an energy gap near the Fermi surface for single-particle levels in 152^{152}Sm with β2=0.14∼0.26\beta_2 = 0.14 \sim 0.26 is found, and the important role of the octupole deformation driving pair ν2f7/2\nu 2f_{7/2} and ν1i13/2\nu 1i_{13/2} is demonstrated.Comment: 11 pages, 3 figure
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