dorsal/arxiv
View SchemaMesoscopic Fluctuations of the Loschmidt Echo
| Authors | Cyril Petitjean, Philippe Jacquod |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410099 |
| URL | https://arxiv.org/abs/quant-ph/0410099 |
| DOI | 10.1103/PhysRevE.71.036223 |
| Journal | Phys. Rev. E 71, 036223 (2005) |
Abstract
We investigate the time-dependent variance of the fidelity with which an initial narrow wavepacket is reconstructed after its dynamics is time-reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that the variance first rises algebraically up to a critical time $t_c$, after which it decays. To leading order in the effective Planck's constant $\hbar_{\rm eff}$, this decay is given by the sum of a classical term $\simeq \exp[-2 \lambda t]$, a quantum term $\simeq 2 \hbar_{\rm eff} \exp[-\Gamma t]$ and a mixed term $\simeq 2 \exp[-(\Gamma+\lambda)t]$. Compared to the behavior of the average fidelity, this allows for the extraction of the classical Lyapunov exponent $\lambda$ in a larger parameter range. Our results are confirmed by numerical simulations.
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"abstract": "We investigate the time-dependent variance of the fidelity with which an\ninitial narrow wavepacket is reconstructed after its dynamics is time-reversed\nwith a perturbed Hamiltonian. In the semiclassical regime of perturbation, we\nshow that the variance first rises algebraically up to a critical time $t_c$,\nafter which it decays. To leading order in the effective Planck\u0027s constant\n$\\hbar_{\\rm eff}$, this decay is given by the sum of a classical term $\\simeq\n\\exp[-2 \\lambda t]$, a quantum term $\\simeq 2 \\hbar_{\\rm eff} \\exp[-\\Gamma t]$\nand a mixed term $\\simeq 2 \\exp[-(\\Gamma+\\lambda)t]$. Compared to the behavior\nof the average fidelity, this allows for the extraction of the classical\nLyapunov exponent $\\lambda$ in a larger parameter range. Our results are\nconfirmed by numerical simulations.",
"arxiv_id": "quant-ph/0410099",
"authors": [
"Cyril Petitjean",
"Philippe Jacquod"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"nlin.CD"
],
"doi": "10.1103/PhysRevE.71.036223",
"journal_ref": "Phys. Rev. E 71, 036223 (2005)",
"title": "Mesoscopic Fluctuations of the Loschmidt Echo",
"url": "https://arxiv.org/abs/quant-ph/0410099"
},
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