Large n limit

The last expression on the RHS is valid in the large N limit. Notice that the expression (69), with (70) is the same as the expression (61) for the two step case, provided we replace the numerical prefactor there (0.798) with (1.436). We illustrate the asymptotic results (69) and (64) in Fig. 4. 

The idea behind the method is the following. We express the probability distribution P W) as a sum over all paths that start from a given initial state. This sum results in a path integral that can be approximated by its dominant solution or classical path in the large N limit, N being the number of particles. The present approach exploits the fact that, as soon as N becomes moderately large, the contribution to the path integral is very well approximated by the classical path. In addition, the classical path exactly satisfies the FT. Here we limit ourselves to show in a very sketchy way how the method applies to solve... 

S.T. Rittenhouse, C.H. Greene, The degenerate Fermi gas with density-dependent interactions in the large-N limit under the K-harmonic approximation, J. Phys. B At. Mol. Opt. Phys. 41 (2008) 205302. 

Although the exponential separation capability persists only for times shorter than the lag time, t., the lag time for such laminates is greatly extended by the partition coefficient (1). That is, in the large n limit for... 

Values of storage modulus G (a)) and loss modulus G"(m) can then be obtained by separating Eq. V-8 into its real and imaginary parts (Eq. V-2). Viscosity and recoverable compliance in the large N limit can be obtained from ... 

We next consider the ideal gas in three spatial dimensions, in the large N limit to test the theory... 

Again, the result for the diffusion coefficient D = 2prpi sx ) /2s.t is the same as in Eq. (7.7) only whenp,. = pi = 1/2. The important observation is, again, that a Gaussian distribution was obtained as an approximation to the actual binomial one in the large N limit. 

The relative positions of the two maxima on the Y surface will change with N, even after accounting for the fact that and 0 are extensive quantities in the large-N limit. The presence of the structure-disrupting surface has a greater influence on an ice phase than on a liquid phase. As N declines, I /N decreases and 0/N increases for both maxima, but the changes are larger for ice than for liquid. Further-... 

At this stage we forget the perturbation character of this result and take the large N limit. We obtain a and... 

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