Fidelity recovery in the Gaussian ensembles (量子系およびマクロ系におけるカオスと非線形動力学)

概要

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この論文は国立情報学研究所の電子図書館事業により電子化されました。Using supersymmetry techniques analytical expressions for the average of the fidelity amplitude f_ε(γ) = 1/NTr[exp(2πιHφγ)exp(-2πιH_0γ)] are obtained, where Hφ = H_0cosφ + H_1sinφ, and H_0 and H_1 are matrices of rank N, taken from the Gaussian unitary ensemble(GUE) or the Gaussian orthogonal ensemble(GOE), respectively. For small perturbation strengths e = 4Nφ^2 a Gaussian decay of the fidelity amplitude is observed, whereas for stronger perturbations a change to a single-exponential decay takes place. Close to the Heisenberg time γ = 1, however, a partial revival of the fidelity is found. It can be interpreted in terms of an spectral analogue of the Debye-Waller factor, describing in X-ray spectroscopy the decrease of von Laue reflexes with increasing temperature.
物性研究刊行会の論文
2005-06-20