In this work we have studied energy flow in acoustic billiards, focusing on irregular billiards with and without current effects. The open systems were modeled with an imaginary potential as a source and drain. We have used the finite difference method to model the billiards. General features of the systems are reported and effects of the measuring probe on the wave function are discussed.
Contents
1 Introduction
2 Theory
2.1 Billiards in general
2.1.1 Classical chaos and billiards
2.2 Acoustics
2.2.1 Basic acoustics
2.2.2 Imaginary potential and energy flow
2.3 Microwave billiards
2.4 Statistics in acoustics
2.4.1 Distribution of eigenvalues
2.4.2 Wave functions and amplitudes
3 Modelling
3.1 Discretization
3.1.1 Finite difference method
3.2 Boundary conditions
3.2.1 Neumann
3.3 Solving the matrix
3.4 Visualisation
3.4.1 Wave intensity
3.4.2 Energy flow arrows
3.4.3 Energy flow densities
4 Results
4.1 General results
4.1.1 Resolution
4.2 Closed billiards
4.2.1 Rectangular billiard
4.2.2 Sinai billiards
4.3 Open billiards
4.3.1 Source and drain
4.3.2 Antenna added
4.4 Statistics extracted from our models
4.4.1 Spacings between energy levels
4.4.2 Wave function statistics
5 Conclusions and future work
5.1 Concluding comments
5.2 Future work
A Derivation of the energy flow
Bibliography
Author: Fälth, Lina
Source: Linköping University
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