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The Quantized Baker's Transformation

The quantal Baker's map is described by a unitary operator acting in a N-dimensional Hilbert space. Its properties are similar to the classical transformation and it becomes that in the classical limit (N → ∞, → 0). The eigenangles are effectively all irrational leading to no recurrences. The quantal and classical time evolutions cease to have any relation to each other for times larger than log2N.