A Parity-Conserving Canonical Quantization for the Baker's Map
msra(1998)
摘要
We present here a complete description of the quantization of the baker's
map. The method we use is quite different from that used in Balazs and Voros
[BV] and Saraceno [S]. We use as the quantum algebra of observables the
operators generated by {exp(2 Pi ix),exp (2 Pi ip)} and construct a unitary
propagator such that as Planck's constant tends to zero,the classical dynamics
is returned. For Planck's constant satisfying the integrality condition 1/N
with N even, and for periodic boundary conditions for the wave functions on the
torus, we show that the dynamics can be reduced to the dynamics on an
N-dimensional Hilbert space, and the unitary N by N matrix propagator is the
same as given in [BV] except for a small correction of order Planck's constant.
This correction is is shown to preserve the symmetry x->1-x and p->1-p of the
classical map for periodic boundary conditions.
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关键词
quantum algebra,hilbert space,periodic boundary condition,satisfiability
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