dorsal/arxiv
View SchemaSemiclassical evaluation of quantum fidelity
| Authors | Jiri Vanicek, Eric J. Heller |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302192 |
| URL | https://arxiv.org/abs/quant-ph/0302192 |
| DOI | 10.1103/PhysRevE.68.056208 |
| Journal | Phys. Rev. E 68, 056208 (2003). |
Abstract
We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform expression is accurate at times when there are 10^70 semiclassical contributions. Remarkably, it also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation (CPA) and show that within this approximation, the so-called ``diagonal approximation'' is automatic and does not require ensemble averaging.
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"abstract": "We present a numerically feasible semiclassical (SC) method to evaluate\nquantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It\nwas thought that such evaluation would be intractable, but instead we show that\na uniform SC expression not only is tractable but it gives remarkably accurate\nnumerical results for the standard map in both the Fermi-golden-rule and\nLyapunov regimes. Because it allows Monte Carlo evaluation, the uniform\nexpression is accurate at times when there are 10^70 semiclassical\ncontributions. Remarkably, it also explicitly contains the ``building blocks\u0027\u0027\nof analytical theories of recent literature, and thus permits a direct test of\nthe approximations made by other authors in these regimes, rather than an a\nposteriori comparison with numerical results. We explain in more detail the\nextended validity of the classical perturbation approximation (CPA) and show\nthat within this approximation, the so-called ``diagonal approximation\u0027\u0027 is\nautomatic and does not require ensemble averaging.",
"arxiv_id": "quant-ph/0302192",
"authors": [
"Jiri Vanicek",
"Eric J. Heller"
],
"categories": [
"quant-ph",
"nlin.CD"
],
"doi": "10.1103/PhysRevE.68.056208",
"journal_ref": "Phys. Rev. E 68, 056208 (2003).",
"title": "Semiclassical evaluation of quantum fidelity",
"url": "https://arxiv.org/abs/quant-ph/0302192"
},
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