dorsal/arxiv
View SchemaA Parity-Conserving Canonical Quantization for the Baker's Map
| Authors | Ron Rubin, Nathan Salwen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9801058 |
| URL | https://arxiv.org/abs/quant-ph/9801058 |
Abstract
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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"abstract": "We present here a complete description of the quantization of the baker\u0027s\nmap. The method we use is quite different from that used in Balazs and Voros\n[BV] and Saraceno [S]. We use as the quantum algebra of observables the\noperators generated by {exp(2 Pi ix),exp (2 Pi ip)} and construct a unitary\npropagator such that as Planck\u0027s constant tends to zero,the classical dynamics\nis returned. For Planck\u0027s constant satisfying the integrality condition 1/N\nwith N even, and for periodic boundary conditions for the wave functions on the\ntorus, we show that the dynamics can be reduced to the dynamics on an\nN-dimensional Hilbert space, and the unitary N by N matrix propagator is the\nsame as given in [BV] except for a small correction of order Planck\u0027s constant.\nThis correction is is shown to preserve the symmetry x-\u003e1-x and p-\u003e1-p of the\nclassical map for periodic boundary conditions.",
"arxiv_id": "quant-ph/9801058",
"authors": [
"Ron Rubin",
"Nathan Salwen"
],
"categories": [
"quant-ph"
],
"title": "A Parity-Conserving Canonical Quantization for the Baker\u0027s Map",
"url": "https://arxiv.org/abs/quant-ph/9801058"
},
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