ترغب بنشر مسار تعليمي؟ اضغط هنا

Scattering approach to fidelity decay in closed systems and parametric level correlations

54   0   0.0 ( 0 )
 نشر من قبل Thomas Gorin
 تاريخ النشر 2012
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

This paper is based on recent work which provided an exact analytical description of scattering fidelity experiments with a microwave cavity under the variation of an antenna coupling [Kober et al., Phys. Rev. E 82, 036207 (2010)]. It is shown that this description can also be used to predict the decay of the fidelity amplitude for arbitrary Hermitian perturbations of a closed system. Two applications are presented: First, the known result for global perturbations is re-derived, and second, the exact analytical expression for the perturbation due to a moving S-wave scatterer is worked out. The latter is compared to measured data from microwave experiments, which have been reported some time ago. Finally, we generalize an important relation between fidelity decay and parametric level correlations to arbitrary perturbations.

قيم البحث

اقرأ أيضاً

Unexpected relations between fidelity decay and cross form--factor, i.e., parametric level correlations in the time domain are found both by a heuristic argument and by comparing exact results, using supersymmetry techniques, in the framework of rand om matrix theory. A power law decay near Heisenberg time, as a function of the relevant parameter, is shown to be at the root of revivals recently discovered for fidelity decay. For cross form--factors the revivals are illustrated by a numerical study of a multiply kicked Ising spin chain.
We study the fidelity decay in the $k$-body embedded ensembles of random matrices for bosons distributed in two single-particle states, considering the reference or unperturbed Hamiltonian as the one-body terms and the diagonal part of the $k$-body e mbedded ensemble of random matrices, and the perturbation as the residual off-diagonal part of the interaction. We calculate the ensemble-averaged fidelity with respect to an initial random state within linear response theory to second order on the perturbation strength, and demonstrate that it displays the freeze of the fidelity. During the freeze, the average fidelity exhibits periodic revivals at integer values of the Heisenberg time $t_H$. By selecting specific $k$-body terms of the residual interaction, we find that the periodicity of the revivals during the freeze of fidelity is an integer fraction of $t_H$, thus relating the period of the revivals with the range of the interaction $k$ of the perturbing terms. Numerical calculations confirm the analytical results.
We derive fidelity decay and parametric energy correlations for random matrix ensembles where time--reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities can be established.
Mean fidelity amplitude and parametric energy--energy correlations are calculated exactly for a regular system, which is subject to a chaotic random perturbation. It turns out that in this particular case under the average both quantities are identic al. The result is compared with the susceptibility of chaotic systems against random perturbations. Regular systems are more susceptible against random perturbations than chaotic ones.
76 - T. Gorin , H. Kohler , T. Prosen 2006
Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution based on expon entiated linear response will be given. For one representative case the exact solution is obtained from a supersymmetric calculation. The results agree well with dynamical calculations for a kicked top.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا