Fractal patterns spotted in the quantum realm
in [Physics]
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From: Sam Wormley on 11 Feb 2010 23:51 Fractal patterns spotted in the quantum realm Electrons interfere to create fractal patterns in ferromagnet http://physicsworld.com/cws/m/1638/17632/article/news/41659
From: Baron on 12 Feb 2010 20:20 "Sam Wormley" <swormley1(a)gmail.com> wrote in message news:b8CdndFLWM71Q-nWnZ2dnUVZ_oudnZ2d(a)mchsi.com... > Fractal patterns spotted in the quantum realm > Electrons interfere to create fractal patterns in ferromagnet > http://physicsworld.com/cws/m/1638/17632/article/news/41659 that is not a fractal pattern. It lacks primary characeteristics of a fractal pattern.
From: nuny on 13 Feb 2010 06:06 On Feb 12, 5:20 pm, "Baron" <nos...(a)invalid.com> wrote: > "Sam Wormley" <sworml...(a)gmail.com> wrote in message > > news:b8CdndFLWM71Q-nWnZ2dnUVZ_oudnZ2d(a)mchsi.com... > > > Fractal patterns spotted in the quantum realm > > Electrons interfere to create fractal patterns in ferromagnet > >http://physicsworld.com/cws/m/1638/17632/article/news/41659 > > that is not a fractal pattern. It lacks primary characeteristics of a > fractal pattern. Chaotic maybe, which is reasonable considering the physics. But no, not fractal. I see no estimate of the structure's fractal dimension. Mark L. Fergerson
From: Sam Wormley on 13 Feb 2010 17:22 On 2/13/10 5:06 AM, nuny(a)bid.nes wrote: > On Feb 12, 5:20 pm, "Baron"<nos...(a)invalid.com> wrote: >> "Sam Wormley"<sworml...(a)gmail.com> wrote in message >> >> news:b8CdndFLWM71Q-nWnZ2dnUVZ_oudnZ2d(a)mchsi.com... >> >>> Fractal patterns spotted in the quantum realm >>> Electrons interfere to create fractal patterns in ferromagnet >>> http://physicsworld.com/cws/m/1638/17632/article/news/41659 >> >> that is not a fractal pattern. It lacks primary characeteristics of a >> fractal pattern. > > Chaotic maybe, which is reasonable considering the physics. > > But no, not fractal. I see no estimate of the structure's fractal > dimension. > > > Mark L. Fergerson Ref: http://www.sciencemag.org/cgi/content/abstract/327/5966/665 "Based on the predictions for the noninteracting limit, we expect critical states to have a spatial structure that is multifractal in nature. This property is directly related to the scale-invariant nature of critical wave functions and has been examined in great detail by numerical simulations of the single-particle quantum states near an Anderson transition (8). Multifractal patterns, which are ubiquitous in nature, are usually described by analysis of their self-similarity at different length scales through their singularity spectrum f(). Physically, f() describes all the fractal dimensions embedded in a spatial pattern, such as those associated with a quantum wave function and its probability distribution. It is calculated by splitting the probability distribution into sets of locations {ri} that share a common exponent , where the distribution scales locally with distance as |(ri)|2 ~ L�, and measuring the fractal dimension of each set (8, 21). A variety of techniques have been developed to compute f(), which has been used to distinguish between various models of the Anderson transition (21, 30). Application of such an analysis to our conductance maps (Fig. 5D, inset) shows an f() spectrum that is peaked at a value away from 2, which is indicative of anomalous scaling in a two-dimensional map. The f() spectrum also shows a systematic shift with decreasing doping, indicating a trend from weak toward strong multifractality with decreasing doping. In contrast, these signatures of multifractal behavior are absent for states deep in the valence band (gray curve) that, despite the strong disorder, show scaling consistent with those expected for extended states".
From: BURT on 13 Feb 2010 23:13
On Feb 13, 2:22 pm, Sam Wormley <sworml...(a)gmail.com> wrote: > On 2/13/10 5:06 AM, n...(a)bid.nes wrote: > > > > > > > On Feb 12, 5:20 pm, "Baron"<nos...(a)invalid.com> wrote: > >> "Sam Wormley"<sworml...(a)gmail.com> wrote in message > > >>news:b8CdndFLWM71Q-nWnZ2dnUVZ_oudnZ2d(a)mchsi.com... > > >>> Fractal patterns spotted in the quantum realm > >>> Electrons interfere to create fractal patterns in ferromagnet > >>>http://physicsworld.com/cws/m/1638/17632/article/news/41659 > > >> that is not a fractal pattern. It lacks primary characeteristics of a > >> fractal pattern. > > > Chaotic maybe, which is reasonable considering the physics. > > > But no, not fractal. I see no estimate of the structure's fractal > > dimension. > > > Mark L. Fergerson > > Ref:http://www.sciencemag.org/cgi/content/abstract/327/5966/665 > > "Based on the predictions for the noninteracting limit, we expect > critical states to have a spatial structure that is multifractal in > nature. This property is directly related to the scale-invariant nature > of critical wave functions and has been examined in great detail by > numerical simulations of the single-particle quantum states near an > Anderson transition (8). Multifractal patterns, which are ubiquitous in > nature, are usually described by analysis of their self-similarity at > different length scales through their singularity spectrum f(). > Physically, f() describes all the fractal dimensions embedded in a > spatial pattern, such as those associated with a quantum wave function > and its probability distribution. It is calculated by splitting the > probability distribution into sets of locations {ri} that share a common > exponent , where the distribution scales locally with distance as > |(ri)|2 ~ L , and measuring the fractal dimension of each set (8, 21). A > variety of techniques have been developed to compute f(), which has been > used to distinguish between various models of the Anderson transition > (21, 30). Application of such an analysis to our conductance maps (Fig. > 5D, inset) shows an f() spectrum that is peaked at a value away from 2, > which is indicative of anomalous scaling in a two-dimensional map. The > f() spectrum also shows a systematic shift with decreasing doping, > indicating a trend from weak toward strong multifractality with > decreasing doping. In contrast, these signatures of multifractal > behavior are absent for states deep in the valence band (gray curve) > that, despite the strong disorder, show scaling consistent with those > expected for extended states".- Hide quoted text - > > - Show quoted text - Fractal angles are nonsense. Mitch Raemsch |