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A discussion of the microscopic components of the membrane demonstrates the relation between the upwards and downwards position of a membrane dipole and the permeability of a segment of interconnected protein subunits. In the model which is proposed, the membrane is assumed to consist of a continuous system of idealized dipoles which have two equilibrium positions, one parallel and one antiparallel to the normal membrane surface. An analogy is made with a magnetic system of Ising spins in a magnetic field. The dynamics of the Ising spin system is then discussed and the results summarized. These results are then used to propose a formula for the sodium conductivity for the equivalent system of dipole channels in the membrane in terms of the fluctuation of these dipoles around the average polarization. The sodium conductance is shown to depend on the rigidity of the channel structure in the presence of an electric field. The results of the numerical calculation based on this model show qualitative agreement with the experimental results of Hodgkin and Huxley's measurements of the sodium current. Copyright © 1975 John Wiley & Sons, Inc.

第Ⅰ部 科学原論 第7章 物理学と社会北原 和夫[国際基督教大学教養学部（学生部長）、日本物理学会会長]

A model is presented for a system of N two-level excitons interacting with each other via optical nearfields represented as localized photons. In a low exciton density limit, quantum dynamics of the dipolemoments or quantum coherence between any two energy levels is linear. As the exciton density becomeshigher, the dynamics becomes nonlinear, and the system has several kinds of quasi-steady states of thedipole distribution depending on the system parameters. These quasi-steady states are classified with thehelp of the effective Hamiltonian that is derived from the renormalization of degrees of freedom oflocalized photons with a unitary transformation. Among them there exist a ‘‘ferromagnetic’’ state(dipole-ordered state), in which all electric dipoles are aligned in the same direction, and an ‘‘anti-ferromagnetic’’ state, where all dipoles alternatingly change the direction. In addition, we show that anarbitrary state can be transformed into a dipole-ordered state by manipulating initial values of thepopulation differences appropriately. For example, if we initially prepare a dipole-forbidden state, whichis similar to the ‘‘anti-ferromagnetic’’ state and cannot be coupled with propagating far fields, and if wemanipulate the distribution of the population differences properly, the initial state evolves into a dipole-ordered state. The radiation property of such dipole-ordered states is examined in detail. Neglectingenergy dissipation by radiation, we find that some of the ordered states show strong radiation equivalentto Dicke’s superradiance. Then by introducing a radiation reservoir, the dissipative master equation isderived. Solving the equation with and without quantum correlations, we numerically show that multiplepeaks in the radiation profile can survive in both cases. The mechanism of this phenomenon is discussed,and a brief comment on an application to photonic devices on a nanometer scale is given.

We study the nonequilibrium spatial correlations of the density fluctuations for a selected reagent as well as the spatial correlations of its energetic states in a stationary state of a model chemical system. In the considered chemical model the reagent of interest appears as a product of a binary process and vanishes as the result of a fast unimolecular decay. Assuming that the lifetime of the reagent is short enough to treat its motion as a ballistic rather than diffusive one we derive analytical formulae for all correlation functions. The results obtained from these formulae agree well with correlations directly measured in molecular dynamics simulations.

Vacancy-assisted diffusion in a crystalline solid can be modeled by means of many particles jumping stochastically to their respective nearest-neighbor lattice-sites with double occupancy forbidden. The diffusion coefficient of a tagged particle, defined in terms of its mean square displacement, depends not only on the transition rate but also on the particle concentration. Nakazato and Kitahara [Prog. Theor. Phys. 64 (1980) 2261] devised a projection operator method to calculate its approximate expression interpolating between the low- and high-concentration limits for a square lattice in any dimension. In this paper, we apply their method to a honeycomb lattice and a diamond lattice, in each of which a set of the nearest-neighbor vectors depends on a site from which they originate. Compared with simulation results, our explicit expression is found to give a good interpolation in each lattice unless the host particles migrate more slowly than the tagged particle.

This paper describes a novel model for the dynamics of the dipole coherence in two-level quantum dots (QDs) interacting with localized photons. The model is based on the fact that the coupling on a nanometer scale between QDs via optical near fields represented by localized photons is much stronger than that via propagating far fields. The model predicts that an intriguing phenomenon such as a collective dipole oscillation occurs if the initial quantum states are locally manipulated. The origin of this kind of collective behaviour is discussed in view of Dicke's superradiance.

In this paper we consider a chemical process, for which the reagent of interest decays shortly after it is created. For such a system the standard theory of nonequilibrium spatial correlations in the density fluctuations, which leads to Ornstein–Zernike type of expression, does not work. We compare results of molecular simulations with another theoretical description based on the assumption that the lifetime of the reagent is short enough to treat its motion as a ballistic rather than diffusive one.

We analyze the exact solution of the recombination probability of a radical pair with the Δg mechanism for the spin dynamics and diffusion for translational motion. This reproduces the B 12 dependence of the recombination probability in a small magnetic field and the saturation effect in a strong magnetic field.

A kinetic model of a reaction–diffusion system by which fluctuation around a nonequilibrium steady state can be analyzed without resorting to a local equilibrium assumption is discussed. The spatial correlation function of concentration fluctuations is analytically calculated, and it is shown that (i) the result is consistent with the previous studies for sufficiently slow chemical reactions, and (ii) how the correlation function is modified when chemical reactions are fast.

The k-dependent hydrodynamic fluctuations for binary classical fluids are discussed. The aim of this paper is to give the microscopic basis for the phenomenological formulation of hydrodynamics of binary fluids which was explored by the present author. The generalized Langevin equation formalism is used to derive closed equations for the fluctuations of temperature, mass, relative velocity, etc. Explicit expressions for the k-dependent thermodynamic susceptibilities are also derived. Using these quantities, it is shown that the equations for fluctuations reduce to the macroscopic equations in the long wavelength limit.

The mesoscopic description of a system with chemical reactions predicts that if the detailed balance condition is not satisfied then spatial correlations between concentrations of reactants may appear. In this paper we use the molecular dynamics technique for reactive hard spheres in order to obtain correlation functions for fluctuations in concentrations of the reactant for a model of an oscillating chemical system. It is shown that these functions depend on time and therefore the local structure of the system oscillates. A comparison between a theory based on the master equation and results of simulations is presented.

北原和夫［東工大・理］

The mesoscopic description of a system with chemical reactions predicts that if the detailed balance condition is not satisfied then the nonequilibrium spatial correlations between concentrations of reactants may appear. The present work is concerned with the dynamics of their growth. We assume that the system is homogeneous at the beginning and study how fast the nonequilibrium correlations develop. The theory based on the master equation is compared with molecular dynamics simulations performed for a model system of “reacting” hard spheres. The qualitative characteristics of the growth of the spatial correlations, predicted by the theory based on a master equation, are confirmed in our simulations. However, this theory fails to give the correct quantitative description of this process.

A general formalism of nonequilibrium thermodynamics of multicomponent fluids is given. Reversible parts of balance equations for the extensive variables are constructed in such a way that the growth rate of the extensive variables are related to their conjugate intensive parameters in an antisymmetric manner. This enables us to give the balance equation for the diffusional flow which plays an important role in the study of superfluidity and complex fluids.

The steady state spatial correlations in reaction-diffusion systems involving many reversible chemical reactions are examined. It has been already discussed that the spatial correlations are related to the breaking of detailed balance in chemical kinetics for both one species and for two species reversible reactions. Here, we focus our attention on how the spatial correlations of concentration fluctuations in a macroscopically homogeneous systems approach to the instability point. The spatial correlations depend strongly on the stability of systems for two species reactions compared to one species reactions.

The mesoscopic description of a system with chemical reactions predicts that if the detailed balance condition is not satisfied, then nonequilibrium spatial correlations between concentrations of reactants may appear. The present work is concerned with molecular dynamics simulations of such correlations in a model system of “reacting” hard spheres. The simulations have shown that if the detailed balance condition is satisfied, then the nonequilibrium spatial correlations are absent. In a steady state for which the detailed balance condition is not satisfied, the nonequilibrium correlations are present and their spatial exponential decay predicted by the theory based on a master equation, is confirmed in our simulations.

Starting from the Langevin equation a nonlinear evolution equation describing the mean square distance of initially close tagged particles in a turbulent medium is obtained. The equation is the same as that derived for a turbulent plasma by Misguich and Balescu using renormalized kinetic theory. The approach is extended to incorporate stable drift in connection with the diffusion of macro particles in a turbulent fluid. The initial ≈t3 and intermediate exponential growth of the mean square distance subsist even under the presence of stable drift in agreement with many confirmed observations.

A solution with cylindrical symmetry for the time-independent two-dimensional Vlasov equation is given numerically. It is demonstrated that, by adding appropriate numbers of particles trapped in potential-energy troughs, which are created by beam particles with definite angular momenta, varieties of localized vortical solutions can be constructed. There are an electron density hole and an ion density hole in the central region. Around these holes, electrons and ions are distributed on rings in the configuration space.

The spin depolarization of a quantum particle in random magnetic field is treated in terms of a path integral in the spin states as well as the translational motion. The path integral of the spin operator, represented in terms of Fermion operators, is performed in the Fermion coherent state representation. An expression for the spin depolarization is obtained for an arbitrary magnetic field distribution. A particular case, in which the magnetic field is oriented in the z -direction and the magnitude is Gaussianly distributed, is considered and the spin decays exponentially in time.

Several approximate solutions for a dynamical model of chemisorption introduced by Yoshimori and Odoi are given and comparison is made with numerical solution of the model

We present a statistical mechanical analysis of electron-ion recombination processes in weakly ionized nonpolar dense media, being based on the model which can explain the external electric field dependence of electron mobility in these media. We derive a diffusion equation by a projection technique from the phase space to the coordinate space where the stationary distribution of electron momentum in an external electric field has been realized. Then we estimate the recombination rate constant from this equation. Here we deal with the system classically as a three-body recombination process.

The stochastic master equation, which describes phenomena of fluctuation and of relaxation in a large system, is reduced to an equation of Hamilton-Jacobi type. The properties of the reduced equation are shown for simplified models of a bistable system and oscillating systems.

A model of an N two-level system interacting with optical near fields is presented. Multiple pulse generation from a dipole-ordered state is predicted, which can be achieved by local state manipulation of an N two-level system. The origins of the phenomenon are discussed by comparison with Dicke’s superradiance.

Summary On the basis of the procedure for controlling the spins of atoms using circularly polarized evanescent light proposed by Hori et al.[(1996) Abstracts of the 1st Asia-Pacific Workshop on Near-field Optics] we discuss the influence of boundary conditions on the probability of spontaneous emission and thus on the spin polarization efficiency, which was not considered in the Hori et al. study. Using the Carniglia–Mandel mode expansion of electromagnetic fields, we derive the spontaneous emission and spin polarization probabilities of atoms near a dielectric surface, and show the atom–surface distance dependence and refractive index dependence. Numerical evaluation for the 6P1/2–6S1/2 transition of a Cs atom indicates an increase in the efficiency of spin polarization by 30%.

Using density operator formalism, we discuss interdot excitation energy transfer dynamics driven by the optical near-field and phonon bath reservoir, as well as coherent excitation dynamics of a quantum dot system. As an effective interaction between quantum dots induced by the optical near-field, the projection operator method gives a renormalized dipole interaction, which is expressed as a sum of the Yukawa functions and is used as the optical near-field coupling of quantum dots. We examine one- and two-exciton dynamics of a three-quantum dot system suggesting a nanometric photonic switch, and numerically obtain a transfer time comparable with the recent experimental results for CuCl quantum dots.

Thermal conduction in a chain of colliding harmonic oscillators, sometimes called the ding-dong model, is investigated. We first argue that this system is equivalent to the Dawson plasma sheet model. Next we show the Lyapunov analysis for this system to characterize its dynamical property. Finally, we reconsider the numerical study of thermal conduction for this system using the Green-Kubo relation and the direct simulation of Fourier law. Both show that thermal conduction is normal in that kappa(N,T) approximately equals N(0), at least, at low temperature in a large system.

The conditions for the emergence of spatial correlations in a nonequilibrium steady state, proposed by Nicolis and Malek Mansour, are examined and generalized to systems involving many reversible chemical reactions. It is found that, by appropriately choosing controllable parameters, we can obtain a nonequilibrium steady state without spatial correlations.

We calculated the spin depolarization of a quantum particle on a linear chain with Larmor frequencies arranged in a Fibonacci series and compared the result with those for alternating and random arrangements of Larmor frequencies. Though the effects of the thermal bath are not included in this calculation, our result implies that the spin depolarization of a quantum particle such as a muon is a useful probe for local magnetic properties of quasicrystals.

A kinetic theory of one-dimensional plasma sheet model (Dawson model) is developed. The Vlasov equation, the Landau equation, and the Balescu–Lenard equation corresponding to this model are derived. For the Vlasov equation, it is shown that the linearized Vlasov equation exhibits a typical behavior of plasmas as in the three-dimensional space. The Landau collision term and the Balescu–Lenard collision term are identically zero. The fact of the vanishing collision term agrees with the behavior of generic one-dimesional systems. In an approximation that the system is in a thermal bath, the derived Landau equation and Balescu–Lenard equation are transformed into the Fokker–Planck equations. Some physical quantities such as thermal conductivity, relaxation rate, etc., are estimated. A discussion on physical meaning of these results, in particular, the zero collision terms, will be given.

小グループ「熱・統計力学の拡張を目指して」5 熱・統計力学の拡張を目指して, 北原和夫［国際基督教大学］長谷川博［茨城大学理学部］＊所属は当時のものを記載

We derive the path integral representation of the conditional probability for a Markovian process starting from the master equation. Existing derivations require both the variable and the transition probability to be extensive. We show that this requirement may be relaxed if Langer's formula for the transition probability is used. We prove that different path integral representations appearing in the literature are in fact equivalent and correspond to various choices of an arbitrary parameter.

We present a model hamiltonian for quantum light-particle diffusion in a lattice which differs from that of previous investigations by the addition of a phonon coupling to the hopping term. In one dimension we derive a set of master equations which is valid in the high-temperature regime and calculate the diffusion coefficient.