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4: An example of 2D isospectral domains. Left and right shapes have identical eigenvalue spectrum, therefore two drums made by these shapes sound exactly the same.
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Can we change the shape of a domain without altering its sizes? By introducing a size-invariant shape transformation, we propose the existence and explore the consequences of a new type of physical effect appearing at the quantum scales, which we call here as "quantum shape effect". By completely separating the shape effects from size effects, we s...
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Context 1
... differences of min-max values in each case are found as 16.0%, 7.0% and 0.7% respectively for Fig. 4.14a, 4.14b and 4.14c. This suggests quantum shape effects have much more dominant behavior for low density conditions where Maxwell-Boltzmann statistics is obeyed. When the degeneracy increases, the influence of shape reduces. This is understandable, because the degeneracy is inversely proportional to the Fermi wavelengths of particles. Like ...
Context 2
... differences of min-max values in each case are found as 16.0%, 7.0% and 0.7% respectively for Fig. 4.14a, 4.14b and 4.14c. This suggests quantum shape effects have much more dominant behavior for low density conditions where Maxwell-Boltzmann statistics is obeyed. When the degeneracy increases, the influence of shape reduces. This is understandable, because the degeneracy is inversely proportional to the Fermi wavelengths of particles. Like ...
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