dorsal/arxiv
View SchemaOn the semiclassical evolution of quantum operators
| Authors | A. M. Ozorio de Almeida, O. Brodier |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502152 |
| URL | https://arxiv.org/abs/quant-ph/0502152 |
Abstract
The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier transform, the chord representation, are, respectively, unitary reflection and translation operators. Thus, the general semiclassical study of unitary operators allows us to propagate arbitrary operators, including density operators, i.e. the Wigner function. The various propagation kernels are different representations of the superoperators which act on the space of operators of a closed quantum system. We here present the mixed semiclassical propagator, that takes translation chords to reflection centres, or vice versa. In contrast to the centre-centre propagator that directly evolves Wigner functions, it is guaranteed to be caustic free, having a simple WKB-like universal form for a finite time, whatever the number of degrees of freedom. Special attention is given to the near-classical region of small chords, since this dominates the averages of observables evaluated through the Wigner function.
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"abstract": "The Heisenberg evolution of a given unitary operator corresponds classically\nto a fixed canonical transformation that is viewed through a moving coordinate\nsystem. The operators that form the bases of the Weyl representation and its\nFourier transform, the chord representation, are, respectively, unitary\nreflection and translation operators. Thus, the general semiclassical study of\nunitary operators allows us to propagate arbitrary operators, including density\noperators, i.e. the Wigner function. The various propagation kernels are\ndifferent representations of the superoperators which act on the space of\noperators of a closed quantum system. We here present the mixed semiclassical\npropagator, that takes translation chords to reflection centres, or vice versa.\nIn contrast to the centre-centre propagator that directly evolves Wigner\nfunctions, it is guaranteed to be caustic free, having a simple WKB-like\nuniversal form for a finite time, whatever the number of degrees of freedom.\nSpecial attention is given to the near-classical region of small chords, since\nthis dominates the averages of observables evaluated through the Wigner\nfunction.",
"arxiv_id": "quant-ph/0502152",
"authors": [
"A. M. Ozorio de Almeida",
"O. Brodier"
],
"categories": [
"quant-ph"
],
"title": "On the semiclassical evolution of quantum operators",
"url": "https://arxiv.org/abs/quant-ph/0502152"
},
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