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Full-Text Articles in Non-linear Dynamics
Periodic State Revivals In Commensurate Waveguide Arrays, Jovan Petrovic, J. J. P. Veerman
Periodic State Revivals In Commensurate Waveguide Arrays, Jovan Petrovic, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
Emerging optical and quantum computers require hardware capable of coherent transport of and operations on quantum states. Here, we investigate finite optical waveguide arrays with linear coupling as means of efficient and compact coherent state transfer. Coherent transfer with periodic state revivals is enabled by engineering coupling coefficients between neighbouring waveguides to yield commensurate eigenvalue spectrum. Particular cases of finite arrays have been actively studied to achieve the perfect state transfer by mirroring the input into the output state.
We explore a much wider scope of coherent propagation and revivals of both the state amplitude and phase. We analytically solve …
On The Spectra Of Certain Directed Paths, Carlos Martins Da Fonseca, J. J. P. Veerman
On The Spectra Of Certain Directed Paths, Carlos Martins Da Fonseca, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We describe the eigenpairs of special kinds of tridiagonal matrices related to problems on traffic on a one-lane road. Some numerical examples are provided.
Hausdorff Dimension Of Boundaries Of Self-Affine Tiles In R N, J. J. P. Veerman
Hausdorff Dimension Of Boundaries Of Self-Affine Tiles In R N, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We present a new method to calculate the Hausdorff dimension of a certain class of fractals: boundaries of self-affine tiles. Among the interesting aspects are that even if the affine contraction underlying the iterated function system is not conjugated to a similarity we obtain an upper- and and lower-bound for its Hausdorff dimension. In fact, we obtain the exact value for the dimension if the moduli of the eigenvalues of the underlying affine contraction are all equal (this includes Jordan blocks). The tiles we discuss play an important role in the theory of wavelets. We calculate the dimension for a …