Next week's seminars

[CM ICTP - Trieste]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR



Tuesday, 10 June -   from 11:00 a.m. to 1 p.m.




Lecture Room 'B' - terrace level-  ICTP Leonardo Building



M. BERRY  ( Bristol University )




Series of lectures on: 'Singularities and asymptotics'


   Seventh lecture


" Quantum mechanics, chaos, and the music of the primes "


Abstract

The Riemann hypothesis can be interpreted as stating that the prime 
numbers contain 'music', whose component frequencies are the Riemann 
zeros.  The question "Frequencies of what?" leads to tantalizing 
connections with the energy levels of quantum systems whose 
corresponding classical motion is chaotic.  At the level of statistics, 
predictions for the Riemann zeros based on semiclassical quantum 
asymptotics (with primes as periods of classical trajectories) have 
reached a high degree of accuracy and refinement.  For the zeros 
themselves, the Riemann-Siegel formula and its improvements lead to new 
ways of calculating quantum levels.

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JOINT ICTP/SISSA CONDENSED MATTER SEMINAR



Seminar Room - ICTP Leonardo Building    (first floor)



Wednesday, 11 June -     4:00 p.m.


M.A. ANISIMOV  (University of Maryland, College Park)


" Novel aspects in thermodynamics of fuzzy interfaces "

Abstract

For decades the behavior of Tolman's length (a curvature-correction 
coefficient in the surface tension [1]) has remained one of the most 
controversial issues in mesoscopic thermodynamics of fluids. Moreover, 
it was commonly believed that Tolman’s length played no significant 
role in practice. However, it was recently shown [2] that there is a 
thermodynamic relation between Tolman’s length and the thickness of the 
interface on the one hand and the shape of the fluid-phase coexistence 
on the other hand. In particular, it was shown that Tolman's length 
strongly diverges at the critical point of fluids with the amplitude 
that depends on the degree of asymmetry in fluid-phase coexistence. The 
critical divergence of Tolman’s length is universal, originating from 
the mesoscopic critical fluctuations. The fluctuations make the fluid 
interface fuzzy and significantly change the shape of the phase 
coexistence. In symmetric systems, such as the lattice gas, the 
curvature correction to the interfacial tension vanishes. The 
divergence of the curvature correction to the interfacial tension is 
especially pronounced in polymer solutions and asymmetric polymer 
blends. Tolman’s length in polymer solutions may become as large as the 
thickness of the smooth interface, thus playing a significant role in 
the behavior of polymer microdroplets and polymer fluids in porous 
media.

[1] R. C. Tolman, J. Chem Phys. 1949, 17, 333.
[2] M. A. Anisimov, Phys. Rev. Lett. 2007, 98, 035702.