Correlation phase transitions

Semiconductor devices ate affected by three kinds of noise. Thermal or Johnson noise is a consequence of the equihbtium between a resistance and its surrounding radiation field. It results in a mean-square noise voltage which is proportional to resistance and temperature. Shot noise, which is the principal noise component in most semiconductor devices, is caused by the random passage of individual electrons through a semiconductor junction. Thermal and shot noise ate both called white noise since their noise power is frequency-independent at low and intermediate frequencies. This is unlike flicker or ///noise which is most troublesome at lower frequencies because its noise power is approximately proportional to /// In MOSFETs there is a strong correlation between ///noise and the charging and discharging of surface states or traps. Nevertheless, the universal nature of ///noise in various materials and at phase transitions is not well understood. 

A fingerprint of a continuous phase transition is the divergence of the correlation length at the critical temperature 7", with for... 

K. Binder, P. C. Hoehenberg. Phase transitions and static spin correlations in Ising models with free surfaces. Phys Rev B 6 3461-3487, 1972. 

Just as in phase transitions in statistical mechanical systems, observable quantities in PCA systems display singularities obeying simple power laws with universal critical exponents at the transition point. For example, letting ni be the number of sites with correlation length, and t be the correlation time, Kinzel [kinz85b] finds that for p ... 

One of the primary features of the Gay-Berne potential is the presence of anisotropic attractive forces which should allow the observation of thermally driven phase transitions and this has proved to be the case. Thus using the parametrisation proposed by Gay and Berne, Adams et al. [9] showed that GB(3.0, 5.0, 2, 1) exhibits both nematic and isotropic phases on varying the temperature at constant density. This was chosen to be close to the transitional density for hard ellipsoids with the same ellipticity indeed it is generally the case that to observe a nematic-isotropic transition for Gay-Berne mesogens the density should be set in this way. The long range orientational order of the phase was established from the non-zero values of the orientational correlation coefficient, G2(r), at large separations and the translational disorder was apparent from the radial distribution function. 

Applying MD to systems of biochemical interest, such as proteins or DNA in solution, one has to deal with several thousands of atoms. Models for systems with long spatial correlations, such as liquid crystals, micelles, or any system near a phase transition or critical point, also must involve a large number of atoms. Some of these systems, including synthetic polymers, obey certain scaling laws that allow the estimation of the behaviour of a large system by extrapolation. Unfortunately, proteins are very precise structures that evade such simplifications. So let us take 10,000 atoms as a reasonable size for a realistic complex system. 

In general terms, the phenomena described above belong to the class of phase transitions and critical phenomena in confined spaces. From the field of statistical physics, some far-reaching results applying to such problems are knovm. One fruitful concept used in statistical physics is the correlation length (see, e.g., [64]). The correlation length describes how a local field quantity evaluated at one point in space is correlated with the same quantity at another point. As an example, the correlation length crfor density fluctuations in a fluid is defined via... 

Hence, close to the critical point thermodynamic quantities at comparatively distant spatial locations become correlated. Especially in the case of liquid micro flows close to a phase transition, these considerations suggest that the correlation length and not the molecular diameter is the length scale determining the onset of deviations from macroscopic behavior. 

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