On some results about the variational theory of complex rays used close to the high frequency regime

2016 ◽  
Vol 124 ◽  
pp. 30-43 ◽  
Author(s):  
Hervé Riou
Keyword(s):  
High Frequency ◽  
Variational Theory ◽  
Frequency Regime ◽  
Complex Rays

scholarly journals A comparison of coarse spaces for Helmholtz problems in the high frequency regime

2021 ◽  
Vol 98 ◽  
pp. 239-253
Author(s):  
Niall Bootland ◽  
Victorita Dolean ◽  
Pierre Jolivet ◽  
Pierre-Henri Tournier
Keyword(s):  
High Frequency ◽  
Frequency Regime

The high-frequency regime

2012 ◽  
pp. 334-374
Author(s):  
C. J. Joachain ◽  
N. J. Kylstra ◽  
R. M. Potvliege
Keyword(s):  
High Frequency ◽  
Frequency Regime

NONCOMMUTATIVE DESCRIPTION OF SPIN HALL EFFECT

2009 ◽  
Vol 06 (02) ◽  
pp. 343-360 ◽  
Author(s):  
AHMED JELLAL ◽  
RACHID HOUÇA
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Hall Effect ◽  
High Frequency ◽  
Hall Conductivity ◽  
Spin Hall Effect ◽  
Harmonic Oscillators ◽  
Frequency Regime ◽  
Basic Features ◽  
Noncommutative Plane

We propose an approach based on a generalized quantum mechanics to deal with the basic features of the intrinsic spin Hall effect. This can be done by considering two decoupled harmonic oscillators on the noncommutative plane and evaluating the spin Hall conductivity. Focusing on the high frequency regime, we obtain a diagonalized Hamiltonian. After getting the corresponding spectrum, we show that there is a Hall conductivity without an external magnetic field, which is noncommutativity parameter θ-dependent. This allows us to make contact with the spin Hall effect and also give different interpretations. Fixing θ, one can recover three different approaches dealing with the phenomenon.

scholarly journals Greybody Factors for Schwarzschild Black Holes: Path-Ordered Exponentials and Product Integrals

Universe ◽  
2018 ◽  
Vol 4 (9) ◽  
pp. 93 ◽  
Author(s):  
Finnian Gray ◽  
Matt Visser
Keyword(s):  
Black Holes ◽  
High Frequency ◽  
Low Frequency ◽  
Intermediate Frequency ◽  
General Context ◽  
Matrix Formalism ◽  
Barrier Penetration ◽  
Frequency Regime ◽  
Transfer Matrix Formalism ◽  
Numerical Approaches

In earlier work concerning the sparsity of the Hawking flux, we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focusing specifically on Schwarzschild black holes, we have re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a pedagogically useful semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, being based on a variant of the “transfer matrix” formalism, are closely related to so-called “product integrals”, leading to quite straightforward and direct numerical evaluation, while side-stepping any need for numerically solving the relevant ordinary differential equations. Furthermore, while considerable analytic information is already available regarding both the high-frequency and low-frequency asymptotics of these greybody factors, numerical approaches seem better adapted to finding suitable “global models” for these greybody factors in the intermediate frequency regime, where most of the Hawking flux is actually concentrated. Working in a more general context, these path-ordered-exponential techniques are also likely to be of interest for generic barrier-penetration problems.

scholarly journals Numerical Eulerian method for linearized gas dynamics in the high frequency regime

2013 ◽  
Vol 127 (4) ◽  
pp. 641-683
Author(s):  
Youness Noumir ◽  
François Dubois ◽  
Olivier Lafitte
Keyword(s):  
High Frequency ◽  
Gas Dynamics ◽  
Eulerian Method ◽  
Frequency Regime

scholarly journals Extended variational theory of complex rays in heterogeneous Helmholtz problem

2017 ◽  
Vol 59 (6) ◽  
pp. 909-918 ◽  
Author(s):  
Hao Li ◽  
Pierre Ladeveze ◽  
Hervé Riou
Keyword(s):  
Variational Theory ◽  
Helmholtz Problem ◽  
Complex Rays
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