Non Saturation of Energy in a Quantum Kicked Oscillator
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We present a quantum mapping for the kicked harmonic oscillator which relates the probability amplitudes of the undriven oscillator's eigenfunctions over successive kicks. We show how for various kick strengths the wave functions have a linear energy increase up to the limit imposed by the finite matrix size of the evolution matrix. We use this linear energy increase to define a quantum diffusion-like coefficient. We also show how this increase in energy causes the wave functions to spread out and become diffuse with little or no discernible structure. This model may serve as a paradigm for the study of quantum chaos.
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