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Discreteness and Equilibrium State Transitions: Novel Insights from Microscopic Fluctuations

Discover the impact of microscopic fluctuations on equilibrium states, including perturbative corrections and phase transition points. Explore groundbreaking concepts by prominent scientists. The novelty lies in the transformative effect of discreteness on final states, redefining life and death scenarios.

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Discreteness and Equilibrium State Transitions: Novel Insights from Microscopic Fluctuations

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  1. R.A. Fisher, Ann. Eugenics 7, 353 ~1937 Kolmogoroff, I.Petrovsky, and N. Piscounoff, Moscow Univ. Bull. Math. 1, 1-1937. P.W. Anderson, Phys. Rev. 109, 1492 ~1958. M. Doi, J. Phys. A 9, 1465 ~1976; H.K. Janssen, Z. Physik. 42, 141 ~1981. P. Grassberger, Z. Phys. B: Condens. Mat 47, 465 ~1982 L. Peliti, J. Phys. ~France! 46, 1469 ~1985. M. Kardar, G. Parisi, and Y.-C. Zhang, PRL 56,889 ~1986. J.L. Cardy and U.C. Tauber, PRL 77, 4780 ~1996 D.C. Mattis, M.L. Glasser, Rev. Mod. Phys. 70, 979 ~1998

  2. Q- Discreteness / microscopic fluctuations were known to • influence the approach to the equilibrium state (e.g. Fisher waves; annihilation) • Make perturbative corrections the value of a phase transition point. • Doi, Janssen, Grassberger, Peliti, Zeldovich, Michailov, Cardy, Mattis and Glasser etc etc • SO What is the novelty? • A- Here the very character of the final state is totally changed (for all values)- Discreteness makes the difference between life and death. N.M. Shnerb, Y. Louzoun, E. Bettelheim, and S. Solomon, Proc. Natl. Acad. Sci. 97, 10322 ~2000.

  3. For Experts(usually they can ask, but in such a big room I have to anticipate their thoughts): Don’t look for cheap escapes: Once a continuous a(x,t) is accepted, the death sentence for la 0 – m< 0is unavoidable Q- slow a(x,t)  a0convergence: A- it is enough a(x,t) < m/ l to have decay at all x Q- non-linear features in PDE b. = (al- m)b + Db D bA-the equation is linear in b Q -instability of the homogenousb(x,t)= b(0,t) solution: A- The solution is stable for la 0 – m< 0

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