%0 Generic %1 stanek2014anomalous %A Stanek, Daniel %A Fauseweh, Benedikt %A Stihl, Christopher %A Pasini, Stefano %A Uhrig, Götz S. %D 2014 %K interesting %T Anomalous behavior of control pulses in presence of noise with singular autocorrelation %U http://arxiv.org/abs/1404.3836 %X We report on the anomalous behavior of control pulses for spins subject to classical noise with a singular autocorrelation function. This behavior is not detected for noise with analytic autocorrelation functions. The effect is manifest in the different scaling behavior of the deviation of a real pulse to the ideal, instantaneous one. While a standard pulse displays scaling $\propto \tau_p^1$, a first-order refocusing pulse normally shows scaling $\tau_p^2$. But in presence of cusps in the noise autocorrelation the scaling $\tau_p^3/2$ occurs. Cusps in the autocorrelation are characteristic for the omnipresent Ornstein-Uhlenbeck process. We prove that the anomalous exponent cannot be avoided; it represents a fundamental limit. On the one hand, this redefines the strategies one has to adopt to design refocusing pulses. On the other hand, the anomalous exponent, if found in experiment, provides important information on the noise properties.

@misc{stanek2014anomalous, abstract = {We report on the anomalous behavior of control pulses for spins subject to classical noise with a singular autocorrelation function. This behavior is not detected for noise with analytic autocorrelation functions. The effect is manifest in the different scaling behavior of the deviation of a real pulse to the ideal, instantaneous one. While a standard pulse displays scaling $\propto \tau_\mathrm{p}^1$, a first-order refocusing pulse normally shows scaling $\propto \tau_\mathrm{p}^2$. But in presence of cusps in the noise autocorrelation the scaling $\propto \tau_\mathrm{p}^{3/2}$ occurs. Cusps in the autocorrelation are characteristic for the omnipresent Ornstein-Uhlenbeck process. We prove that the anomalous exponent cannot be avoided; it represents a fundamental limit. On the one hand, this redefines the strategies one has to adopt to design refocusing pulses. On the other hand, the anomalous exponent, if found in experiment, provides important information on the noise properties.}, added-at = {2014-04-16T04:31:53.000+0200}, author = {Stanek, Daniel and Fauseweh, Benedikt and Stihl, Christopher and Pasini, Stefano and Uhrig, Götz S.}, biburl = {https://www.bibsonomy.org/bibtex/28221b87436dd569e907f6844274c9e71/scavgf}, description = {Anomalous behavior of control pulses in presence of noise with singular autocorrelation}, interhash = {2212e17980827b5a173e760bbb8474f6}, intrahash = {8221b87436dd569e907f6844274c9e71}, keywords = {interesting}, note = {cite arxiv:1404.3836Comment: 11 pages, 8 figures}, timestamp = {2014-04-16T04:31:53.000+0200}, title = {Anomalous behavior of control pulses in presence of noise with singular autocorrelation}, url = {http://arxiv.org/abs/1404.3836}, year = 2014 }