Gaussian energy distributions

Fig. 42 Time-of-flight signals for N2 at three laser fluences. A curve fit to the data using a Gaussian energy distribution for the shoulder and Eq. 16 for the slow peak is shown in the light, broad line the individual fast and slow components are shown in dark lines. REPRINTED WITH PERMISSION OF [Ref. 324], COPYRIGHT (1999) American Institute of Physics...

Fig. 5 The steady-state occupation probability as a function of site energy, for sites with a Gaussian energy distribution. The curves show the fitted Fermi-Dirac functions. The inset shows the same data on a logarithmic scale...

Arkhipov VI, Heremans P, Emelianova EV, Adriaenssens GJ (2001) Space-charge-limited currents in materials with Gaussian energy distributions of localized states. Appl Phys Lett 79(25) 4154 156... 

Amadei, A., Apol, M. E. F., Di Nola, A., Berendsen, H. J. C. The quasi-Gaussian entropy theory Free energy calculations based on the potential energy distribution function. J. Chem. Phys. 104 (1996) 1560-1574... 

If Restart is not checked then the velocities are randomly assigned in a way that leads to a Maxwell-Boltzmann distribution of velocities. That is, a random number generator assigns velocities according to a Gaussian probability distribution. The velocities are then scaled so that the total kinetic energy is exactly 12 kT where T is the specified starting temperature. After a short period of simulation the velocities evolve into a Maxwell-Boltzmann distribution. 

Check. Use the Crooks relation (5.35) to check whether the forward and backward work distributions are consistent. Check for consistency of free energies obtained from different estimators. If the amount of dissipated work is large, caution may be necessary. If cumulant expressions are used, the work distributions should be nearly Gaussian, and the variances of the forward and backward perturbations should be of comparable size [as required by (5.35) for Gaussian work distributions]. Systematic errors from biased estimators should be taken into consideration. Statistical errors can be estimated, for instance, by performing a block analysis. 

FIGURE 8.5 Variation of the b-value of the gaussian thermalization distribution in n-hexane with excess electron energy. While the b values were obtained by comparison with experimental results, other forms of initial distribution are also possible. Reproduced from Hirata and Mataga (1991). 

This implies that the exponents and y defined above are 0 = y = 2( = d) for a first-order transition. Since the symmetry around if = 0 is preserved for finite L, there is no shift of the transition. This feature is different, however, if we consider temperature-driven first-order transitions , since there is no symmetry between the disordered high-temperature phase and the ordered low-temperature phase. In order to understand the rounding of the delta-function singularity of the specific heat, which measures the latent heat for L- oo, it now is useful to consider the energy distribution, for which again a double Gaussian approximation applies ... 

Figure 1. Cummulative distribution of KII data with energies distributed according to a Gaussian. Curve with x is obtained by randomizing the time of the neutrinos.

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