DYE-MEMBRANE INTERACTION AND ITS CHANGES DURING NERVE EXCITATION

Abstract— With a view toward elucidating the physiocochemical properties of the nerve membrane, the behavior of various dye molecules incorporated into the membrane was investigated. By measuring the difference between the absorption spectra of dyes in the membrane at rest and those during nerve excitation, the nature of the conformation changes of the membrane macromolecules were examined. Mathematical expressions were developed describing the absorbance changes of dye molecules during nerve excitation. Experimental evidence was presented indicating that there is, during nerve excitation, rotation of dye molecules in the membrane. The physicochemical bases of the process of production of fluorescence changes during nerve excitation are discussed. Based on the results of measurements of the polarization of the fluorescent light, the existence of a highly ordered macromolecular structure at or near the inner surface of the membrane was inferred.     

Representation of Nonequilibrium Steady States in Large Mechanical Systems

Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the “degree of nonequilibrium”, and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order.     

Integral Geometry of Real Surfaces in the Complex Projective Plane

We give a Poincaré formula for any real surfaces in the complex projective plane which states that the mean value of the intersection numbers of two real surfaces is equal to the integral of some terms of their Kähler angles.     

Hubbard model and the origin of ferromagnetism

It is believed that strong ferromagnetic orders in some solids are generated by subtle interplay between quantum many-body effects and spin-independent Coulomb interactions between electrons. Here we describe our rigorous and constructive approach to ferromagnetism in the Hubbard model, which is a standard idealized model for strongly interacting electrons in a solid.     

On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models

We analyze some solvable models of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. We apply Nakajima-Zwanzig’s projection method by choosing a reference state of the reservoir endowed with the mixing property. In van Hove’s limit, the dynamics is described in terms of a master equation. We observe that Markovianity becomes a valid approximation for timescales that depend both on the form factors of the interaction and on the observables of the reservoir that can be measured.