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Abstract

We investigate the wave energy distribution in complex built-up structures it is clear where the semiclassical approximations are made at each stage of the derivation. We reformulate the boundary integral equations for the Helmholtz equation in terms of incoming and outgoing boundary waves independently of the boundary conditions and decomposing the green functions into singular and regular components. For demonstration purposes, we apply a semiclassical form of the operator (corresponding to a high-frequency approximation) to polygonal coupled-cavity configurations with abrupt changes of the material properties (such as wave speed and absorption coefficients at the interfaces between the cavities)

Keywords

• Bogomolny transfer operator with multiple interfaces at which the material properties change discontinuously. We Boundary integral equations Green function formulate the transfer operator in such a way that it can in principle be made exact, and

Semiclassical Transfer Operator for Complex Built-up Structures

Abstract

We investigate the wave energy distribution in complex built-up structures with multiple interfaces at which the material properties change discontinuously. We formulate the transfer operator in such a way that it can in principle be made exact, and it is clear where the semiclassical approximations are made at each stage of the derivation. We reformulate the boundary integral equations for the Helmholtz equation in terms of incoming and outgoing boundary waves independently of the boundary conditions and decomposing the green functions into singular and regular components. For demonstration purposes, we apply a semiclassical form of the operator (corresponding to a high-frequency approximation) to polygonal coupled-cavity configurations with abrupt changes of the material properties (such as wave speed and absorption coefficients at the interfaces between the cavities).

Keywords

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References

1. M. Abramowitz, I. A. Stegun “Handbook of Mathematical Functions” Dover, New York (1972)
2. H. Ben Hamdin “Boundary element and transfer operator methods for multi-component wave systems” PhD Thesis, School of Mathematical Sciences, Nottingham University, UK( 2012)
3. H. Ben Hamdin, G. Tanner “Multi-component BEM for the Helmholtz equation - A normal derivative method” IOS Press, Shock and Vibration, 19 (2012) 957–967
4. E.B. Bogomolny “Semiclassical quantization of multidimensional systems” Nonlinearity, 5(1992) 805–866
5. P. A. Boasman “Semiclassical Accuracy for Billiards” Nonlinearity, 7 (1994) 485
6. S. C. Creagh, H. Ben Hamdin and G. Tanner “In-out decomposition of boundary integral equations” J.Phys. A: Math. Theor., 46(2013)
7. B. Georgeot, R. E. Prange “Exact and Quasiclassical Fredholm Solutions of Quantum Billiards” Phys. Rev. Lett.,74 (15) (1992) 2851–2854
8. B. Georgeot, R. E. Prange “Fredholm Theory for

9. Quasiclassical Scattering” Phys. Rev. Lett.,74 (21) (1995) 4110–4113
10. T. Prosen “Exact quantum surface of section method” J. Phys. A:Math. Gen., 27(1994)L709– L714
11. T. Prosen “General quantum surface-of-section
12. method” J. Phys. A:Math. Gen., 28(1995) 4133–4155