The quantized Baker's transformation

摘要: Abstract A quantum analogue of the Baker's transformation is constructed using a specially developed quantization procedure. We obtain unitary operator acting on an N-dimensional Hilbert space, with N finite (and even), that has similar properties to classical baker's map, and reduces it in limit, which corresponds here → ∞. The can be described as very simple, fully explicit × matrix. Generalized maps are also quantized studied. Numerical investigations confirm this model nontrivial features ought represent quantal manifestations chaoticity. quasi-energy spectrum given by irrational eigenangles, leading no recurrences. Most eigenfunctions look irregular, but some exhibit puzzling regular features, such peaks at coordinate values belonging periodic orbits map. compare time-evolutions, applied initially coherent quasi-classical states: evolving states stay close agreement for short times seem lose all relationship each other beyond critical time order log 2 ∼ − h .