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001     187509
005     20240619092101.0
024 7 _ |a 10.1016/j.jmr.2014.06.009
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037 _ _ |a FZJ-2015-01138
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|a Stanek, Daniel
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245 _ _ |a Anomalous behavior of control pulses in presence of noise with singular autocorrelation
260 _ _ |a Amsterdam [u.a.]
|b Elsevier
|c 2014
336 7 _ |a Journal Article
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520 _ _ |a 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.
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