Distance geometry higher dimensional

In retrospect, one can see why any attempt to represent the wave-function of a many-electron system by a system of point particles should give a geometry which can t be visualized in three-space. For example, any set of representative (as opposed to instantaneous) interparticle distances, such as a set of expectation values, will generally define a structure which is higher than three-dimensional. In fact, the set of expectation values for an iV-electron atom can be expected to define an iV-dimensional figure, just like the subhamiltonian minimum. 

In a random conductive network, the exponent t does not depend on the lattice geometry details, but only depends on the dimensionality of the network [27]. This is called universal percolation behavior. Theory calculation shows that t 1-1.3 and t 2.0 correspond to two- and three-dimensional networks, respectively. However, many experimental studies reported a wide range of t value from 1 to 12 [19, 28]. Some studies claim that a lower t value is caused by a narrow tunneling distance distribution in the composite system and that a higher t value is caused by abroad tunneling distance distribution. Nevertheless, the difference between the theoretical prediction and the experimental results is still an unresolved issue. 

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