scholarly journals Dirichlet boundary condition for the Lee–Wick-like scalar model

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
L. H. C. Borges ◽  
A. A. Nogueira ◽  
E. H. Rodrigues ◽  
F. A. Barone
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Gauge Field ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Image Method ◽  
Scalar Model ◽  
Scalar Charge ◽  
Klein Gordon

AbstractLee–Wick-like scalar model near a Dirichlet plate is considered in this work. The modified propagator for the scalar field due to the presence of a Dirichlet boundary is computed, and the interaction between the plate and a point-like scalar charge is analysed. The non-validity of the image method is investigated and the results are compared with the corresponding ones obtained for the Lee–Wick gauge field and for the standard Klein–Gordon field.

DEVIATION FROM THE THERMAL EQUILIBRIUM OF THE ACCELERATED DETEKTOR DUE TO THE FIELD THEORETICAL DIVERGENCE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 1026-1032
Author(s):  
NORIKAZU SUZUKI
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Response Function ◽  
Dirichlet Boundary Condition ◽  
Thermal Equilibrium ◽  
Dirichlet Boundary ◽  
Flat Space ◽  
Finite Amount ◽  
Equilibrium Property

We investigate the influence of the field-theoretical divergence on the thermal equilibrium property by employing the model of a uniformly accelerated monopole detector nonlinearly coupled to a scalar field in the flat space with the Dirichlet boundary condition. Introducing the Gaussian switching factor to the interaction between the detector and the field, we estimate the correction to the response function coming from this swithing factor. We find that the deviation from the thermal equilibrium of the response of this detector is mostly due to the interplay between the divergence and the existence of the boundary, when the detector is kept switched on during a large but finite amount of time.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

On the Dispersive Estimate for the Dirichlet Schrödinger Propagator and Applications to Energy Critical NLS

2014 ◽  
Vol 66 (5) ◽  
pp. 1110-1142
Author(s):  
Dong Li ◽  
Guixiang Xu ◽  
Xiaoyi Zhang
Keyword(s):  
Boundary Condition ◽  
Fundamental Solution ◽  
Unit Ball ◽  
Dirichlet Boundary Condition ◽  
Obstacle Problem ◽  
Dirichlet Boundary ◽  
Radial Symmetry ◽  
Well Posedness ◽  
Robust Algorithm ◽  
Dispersive Estimate

AbstractWe consider the obstacle problem for the Schrödinger evolution in the exterior of the unit ball with Dirichlet boundary condition. Under radial symmetry we compute explicitly the fundamental solution for the linear Dirichlet Schrödinger propagator and give a robust algorithm to prove sharp L1 → L∞ dispersive estimates. We showcase the analysis in dimensions n = 5, 7. As an application, we obtain global well–posedness and scattering for defocusing energy-critical NLS on with Dirichlet boundary condition and radial data in these dimensions.

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