1988 Fiscal Year Final Research Report Summary
Statistical Mechanics of Phase Transitions Induced by Topological Excitations.
| Project/Area Number |
61540259
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Institute of Physics, College of Arts and Sciences, University of Tokyo. |
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Principal Investigator |
IZUYAMA Takeo College of Arts and Sciences, University of Tokyo, 教養学部, 教授 (10012288)
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| Project Period (FY) |
1986 – 1988
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| Keywords | Statistical mechanics of an assembly of strings / Thermal fluctuation of membranes / Entropy mechanism / Dislocation theory of melting |
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| Research Abstract |
This research project is to extend the statistical mechanical theory of biomembrane phase transitions developed by Izuyama(1982) to various fields of condensed matter physics. Certain new theoretical aspects have been found, and various new results have been obtained through this project.
(1) Dynamics of biomembrane phase transitions:
The basic variables are the space-dependent disorder parameter and the separations between hydrocarbon chains. The disorder parameter is essentially the local density of the topological excitations which are the strings composed of the kinks and vacancies. The pseudo-criticality predicted by Izuyama-Akutu(1982) is the central problem here. Another problem : A membrance itself is a topological entity for which thermal fluctuations and stability are current subjects of high interest. I have investigated this problem on the basis of the renormalization group theory( J. Phys. Soc. Jpn.(1987)).
(2) Dynamics of proteins in biomembranes:
This has been investigated,f
… More
irst,on the basis of hydrodynamical model, and,second, by means of a new stochastic model. In the latter approach, a new concept called "Entropy Bag" has been discovered.
(3) Terrace-Step-Kink system (TSK) on the surface of a crystal:
Here again the strings are the topological excitations. These strings are two-dimensional topological entities which are called "steps". The strings are modulated everywhere by the kinks. The facet edge is interpreted as the phase transition of such TSK system. The sharpness of the edge can be interpreted as the critical exponent.
(4) Dislocations and disclinations thermally excited in a crystal near melting :
A complete statistical mechanical description of this problem has been published in J. Phys. Soc. Jpn.(1988). Melting of an idealistic crystal composed of infinitely long polymers has also been investigated. Here the string model holds exactly. The two-dimensional model is rigorously solved and has been published in J. Phys. Soc. Jpn.(1988).
(5) Theory of High T_c superconductivity :
This is a unique field of stati-stical physics, where topological excitations play crucial roles. A theory of fundamental mechanism of such superconductivity has been given(J. Phys. Soc. Jpn. 1988 and 1989). Less
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