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@ARTICLE{Stanek:187509,
      author       = {Stanek, Daniel and Fauseweh, Benedikt and Stihl,
                      Christopher and Pasini, Stefano and Uhrig, Götz S.},
      title        = {{A}nomalous behavior of control pulses in presence of noise
                      with singular autocorrelation},
      journal      = {Journal of magnetic resonance},
      volume       = {245},
      issn         = {1090-7807},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier},
      reportid     = {FZJ-2015-01138},
      pages        = {133 - 142},
      year         = {2014},
      abstract     = {We report on the anomalous behavior of control pulses for
                      spins under spin–spin relaxation and 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 View the MathML source∝τp1, a
                      first-order refocusing pulse normally shows scaling View the
                      MathML source∝τp2. But in presence of cusps in the noise
                      autocorrelation the scaling View the MathML source∝τp3/2
                      occurs. Cusps in the autocorrelation are characteristic for
                      fast fluctuations in the noise with a spectral density of
                      Lorentzian shape. 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.},
      cin          = {ICS-1 / Neutronenstreuung ; JCNS-1},
      ddc          = {550},
      cid          = {I:(DE-Juel1)ICS-1-20110106 / I:(DE-Juel1)JCNS-1-20110106},
      pnm          = {451 - Soft Matter Composites (POF2-451) / 54G - JCNS
                      (POF2-54G24)},
      pid          = {G:(DE-HGF)POF2-451 / G:(DE-HGF)POF2-54G24},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000340690300018},
      pubmed       = {pmid:25036295},
      doi          = {10.1016/j.jmr.2014.06.009},
      url          = {https://juser.fz-juelich.de/record/187509},
}