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Spin Seebeck coefficient in a quantum wire is microscopically derived using the Kubo formula and thermal Green’s functions, taking account of the effects of disorder in a self-consistent t-matrix a...

Electron transport is investigated theoretically for an electron which is coupled to a localized spin system. The dc electrical conductivity of spin-fermion models in one dimension is studied by the direct numerical estimation of the Kubo formula. The dependence of the conductivity on temperature and external magnetic field is investigated. When the localized spins are antiferromagnetically coupled on a chain, the conductivity shows a monotonic increase with magnetic field, which is ordinary magnetoresistance. However, in a system where the localized spins form an antiferromagnetically coupled two-leg ladder, the conductivity shows an anomalous non-monotonic field dependence. Analysis of the spin configuration of the localized spin system reveals that quantum fluctuation determines the conductivity through a dimerized-rung spin configuration, and the formation of local triplets on the ladder rungs causes the decrease in conductivity.

The field- and frequency-dependence of Electron Spin Resonance (ESR) in the Shastry–Sutherland lattice with small Dzyaloshinsky–Moriya (DM) interaction is studied by the direct numerical estimation of the Kubo formula. Beside the strong paramagnetic resonance, we find the resonance due to the transitions between the triplet and singlet levels which are prohibited in the case without the DM interaction. Furthermore, we find the resonance which is distributed in a wide range of the field for a specific frequency, which corresponds to the transition between the states with the same magnetization.

Nonequilibrium energy transport phenomena are studied using molecular dynamics simulation. The system is made of hard-core particles which contact with the heat baths at the both ends: hot at left end, and cold at right end. In case of fluid, normal (Fourier-type) heat conduction is reproduced in three-dimensional system, but it is not observed in lower-dimensional systems. In solid–fluid coexisting state, the property of energy transport is different between each phase. Fourier-type heat conduction is reproduced, but the solid phase has larger thermal conductivity than the fluid phase. When hydrodynamic shear is induced at hot end, temperature profile of fluid phase is parabolic form but that of solid phase is straight one. These results suggest that continuum description can be applicable to much shorter length scales (for example, micrometer- or nanometer-scale technology) and in contrast, molecular dynamics approach in such scale systems can be used to study nonequilibrium macroscopic phenomena.

The field and temperature dependence of the line shape of ESR for strongly interacting quantum spin systems would provide various important informations for the magnetic interaction. We have introduced a method of direct numerical estimation of the dynamical susceptibility with the Kubo formula and applied it to spin systems of various lattice structures. There the ESR line shape shows significant dependence on the strength of the field, and also on the geometrical situation among the directions of the fields and lattice axes.

Using the semiclassical Kubo formula for conductivity, we give a periodic-orbit picture for the recently observed fractal magnetoconductance fluctuations in submicron-scale phase coherent ballistic billiards. The self-similar conductance fluctuations are shown to be caused by the self-similar unstable periodic orbits which are generated through a sequence of isochronous pitchfork bifurcations of straight-line librating orbits oscillating towards harmonic saddles. The saddles are naturally created right at the point of contact with the leads or at certain places in the cavity as a consequence of the softwall confinement. Therefore, our mechanism is able to explain all the self-similar magnetoconductance fluctuations in general softwall billiards. In contrast to the existing theory which claims that a classical mixed phase space is necessary, we argue that, even in the fully chaotic phase space, the self-similar magnetoconductance fluctuations should be observed as long as the self-similar unstable periodic...

The resistivity due to Coulomb interaction of two-dimensional electron gas under spatially alternating magnetic field has been calculated based on the Kubo formula. It is found that, in the presence of disorder, the interplay between the periodic potential and the Coulomb interactions results in a T 2 -term in the Drude conductance, which is not due to the Umklapp scattering. The results are in reasonable agreement with experiments by Kato et al. [J. Phys. Soc. Jpn. 68 (1999) 1492].

We investigate the electric and thermal transport properties in a disordered Weyl ferromagnet on an equal footing by using the Keldysh formalism in curved spacetime. In particular, we calculate the anomalous thermal Hall conductivity, which consists of the Kubo formula and the heat magnetization, without relying on the Wiedemann-Franz law. We take nonmagnetic impurities into account within the self-consistent $T$-matrix approximation and reproduce the Wiedemann-Franz law for the extrinsic Fermi-surface and intrinsic Fermi-sea terms, respectively. This is the first step towards a unified theory of the anomalous Hall effect at finite temperature, where we should take into account both disorder and interactions., 18 pages, 7 figures

Electron spin resonance in an antiferromagnetic cluster is studied by a direct numerical method to obtain the dynamical susceptibility χ''(ω) expressed by the Kubo formula. Temperature dependence of the dipolar broadening is investigated in the isotropic Heisenberg model. The width decreases monotonically as the temperature decreases in the case of high frequency. In the case of low frequency, however it is found to show non-monotonic dependence. The frequency- and temperature-dependence of the resonant field of Ising-like Heisenberg model is studied, and it is compared with the conventional antiferromagnetic resonance (AFMR). It is found that the paramagnetic resonance (PMR) coexists with the antiferromagnetic resonance in the wide range of the temperature when the field is applied parallel to the easy axis. A branch of the conventional AFMR is found to split into double peaks. In the case of the field perpendicular to the easy axis, PMR is very broad and disappears at low temperature.

The quantum interference effect in ballistic antidot lattices under a very weak magnetic field is investigated. The area distribution of coherent backscattering orbits obeys the many-peaked structure with each peak located at multiples of the unit-cell area, and can be explained in terms of the length distribution. Using the area distribution in a semiclassical description of Kubo formula, we derive expressions for both h /2 e oscillation and negative magneto-resistivity caused by the interference between a time-reversal pair of coherent backscattering orbits. The flux dependence of the oscillation part in the quantum correction, which qualitatively differs from the one for a single Sinai billiard, is responsible for trapping and jumping motions in the underlying classical dynamics.

The effects of randomness on the tunnel conductance and the tunnel magnetoresistance (TMR) are studied theoretically for ferromagnetic tunnel junctions. An emphasis is put on a combined effects of the interfacial randomness and the electronic structures of the metallic leads. The conductance is formulated by taking the randomness into account at T =0 K and zero bias limit by using the Kubo formula and the coherent potential approximation in a single orbital tight-binding model. The vertex correction to the conductance is calculated so as to satisfy the current conservation law. The tunnel conductance and the TMR with and without randomness are found to depend on the Fermi energy E F and the shape of the Fermi surface. The TMR is affected by the randomness in such a way that it can be increased by the randomness when E F is close to the band bottom, while it is decreased when E F is higher. The variation of the TMR with the barrier height and thickness is also calculated.

We propose a direct numerical method to calculate the dynamical susceptibility, χ''(ω), in strongly fluctuating quantum systems, where the system is nonmagnetic but the exchange effect is very stro...

Analytic expressions for the absorption coefficient of a weak Electromagnetic Wave (EMW) by free carriers for the case of electron-optical phonon scattering in quantum wells are calculated by the Kubo-Mori method in two cases: –The absence of a magnetic field. –The presence of a magnetic field applied perpendicular to its barriers. A different dependence of the absorption coefficient on the temperature T of system, the electromagnetic wave frequency ω, the cyclotron frequency Ω (when a magnetic field is present), and characteristic parameters of a quantum well in comparison with normal semiconductors is obtained. The analytic expressions are numerically evaluated, plotted and discussed for a specific quantum well AlAs/GaAs/AlAs.

It is demonstrated that the finite-time scaling approach, derived from the forced oscillator method, to determine the exponent of the ac conductivity σ(ω)∝ω δ near the metal-insulator transition point is a very powerful method for evaluating the precise value of the exponent δ with high speed and accuracy.

Electron conduction in one-dimensional system is investigated explicitly taking into account the reservoirs to which 1D channel is connected at its ends. We calculate the current driven by the chemical potential difference of two reservoirs, using the linear response theory by Kubo. At 0K, the conductance of 1D channel is expressed in terms of one-electron Green's functions even in the presence of the interaction, in contrast to the theory based on Kubo formula, in which two-electron Green's functions are essentially involved. The formalism in this paper provides a new interpretation of Landauer formula. As regards the interaction effects, the conductance of Fermi liquid without potential scattering is 2 e 2 / h , while that of Tomonaga-Luttinger liquid deceases with power low as the length of 1D channel increases.

A model for the mechanism of ionic conductivity in the high temperature paraelastic phase of M 3 H(XO 4 ) 2 [M=Rb, Cs, X=S, Se] type crystals is proposed. The key features of the conduction mechanism are the following; (1) two kinds of defect states, H 2 XO 4 (+e) and XO 4 (-e) , are formed thermally by breaking of a hydrogen-bond, (2) the H 2 XO 4 (+e) defect state and the XO 4 (-e) defect state move coherently from an XO 4 tetrahedron to a distant XO 4 as the result of successive proton tunneling among hydrogen-bonds. The density of states and the mobility are calculated for the coherent motions of these defect states by the recursion method and the Kubo formula, respectively. The density of states shows the characteristic feature of the Bethe lattice, i.e., the twin peak structure due to self-similarity, while the conductivity is obtained as an order of a magnitude of 10 -3 Ω -1 cm -1 at the ferroelastic transition temperature, consistent with experiments.

Electrical conductivity σ(ω, T ) of a lattice electron system due only to mutual Coulomb interaction is studied on the basis of the Fermi liquid theory, ω and T being the external frequency and the temperature, respectively. Based on the Kubo formula to respect the consistency between the selfenergy and the vertex corrections, a formulation of σ(ω, T ) is given in terms of memory function which is extended to the matrix form. In this formulation, it is explicitly demonstrated that, in the absence of Umklapp processes, T 2 -term in the resistivity vanishes as it should in spite of the fact that the total current is not conserved.

By using the closed-form solution of the Mori formula for transport coefficients obtained very recently, the Mori formula and the Kubo formula have been proved to be identical to each other formally. However, once any approximation procedure is introduced, there may appear some discrepancy between these formula. Then, as for typical examples, we calculate the Mori formula and the Kubo formula for the optical conductivity in a free electron system with impurity scattering and for that in a U -infinite d - p model in some approximate ways and show that both formula coincide with each other practically and the memory function approximation which has been often employed as one of the most important applications of the Mori formula is justified only in the high frequency limit. These results suggest that the Mori formula is no more convenient to be used for calculating transport coefficients than the Kubo formula.

The scaling behavior of dc conductivity σ x x in a current perpendicular to the magnetic field near a vortex-glass (VG) transition is addressed in terms of the Ginzburg-Landau (GL) model and Kubo formula and by assuming a universal scaling behavior of the VG correlation function. Together with the uncorrelated T c -disorder, we also take account of another type of uncorrelated disorder which becomes a familiar expression once assuming the phase-only approximation. Based on a calculation perturbative in the pinning disorders, we show that both of these uncorrelated disorders are necessary in order to obtain the universal scaling of σ x x proposed by Fisher et al . [Phys. Rev. B 43 (1991) 130], and that, if either of them is negligible, the scaling behavior of σ x x can be apparently nonuniversal even deep in the VG critical region. Our results explain, without invoking a possible destruction of true VG transition due to screening, why the vanishing resistivity data show a nonuniversal behavior with a field...

Numerical simulations are performed on the electron transport through random arrays of antidots in a magnetic field. Using the linear response theory, we reproduce two features which were clearly observed in experiments, that is, (1) disappearance of a peak in the magnetoresistivity of random antidot arrays and (2) anisotropy of the magnetoresistivities of anisotropically random arrays. Further we illustrate that the anisotropy is closely related to the characteristic diffusion of the electron.

The present authors have obtained a closed-form solution to the Mori formula for transport coefficients expanded in terms of the projection operator most recently. The present article supplements the previous work by confirming the equivalence between the Mori formula and the Kubo formula unambiguously through evaluating the optical conductivity for a free two-band model explicitly.

Three decades ago, the quantum Langevin equation (Mori formula) was used to reformulate the linear response theory (Kubo formula). Since then, the Mori formula has often been used to evaluate transport coefficients, but only within the Born approximation. In the present study, we obtain a rigorous expression for the transport coefficients as a series expansion in terms of the projection operator. We then evaluate the optical conductivity for a free electron system with impurity scattering in order to discuss the mutual consistency between the Mori formula and the Kubo formula.

The effect of on-site Coulomb repulsion on the process of resonant tunneling through a small interacting region is studied in the presence of a magnetic field by using the recursive Green's function method within a mean field approximation. The conductance is calculated as a function of the chemical potential µ making use of the Kubo formula, and calculations are performed for single- and double-mode quasi-one-dimensional quantum wires. In a magnetic field, some resonance levels close each other to form a single Landau level, so that the electron correlation in the small region is enhanced, and the µ-dependence of the conductance is changed by rather small value of the Coulomb repulsion. For the double-mode wire a collinear-type electronic state, in which spins in the small region are aligned antiferromagnetically in the x -direction and ferromagnetically in the y -direction, is found to be stable over a wide range of the chemical potential.

Using the Kondo lattice model with classical spins in infinite dimension, conductivity in the perovskite-type $3d$ transition-metal oxide (La,Sr)MnO$_3$ is theoretically studied. Green's functions as well as spontaneous magnetization are obtained exactly on the Bethe lattice as a function of temperature. Conductivity is calculated from the Kubo formula. Below the Curie temperature, resistivity as a function of magnetization is in a good agreement with the experimental data. Anomalous behaviour in the temperature dependence of the optical conductivity observed in (La,Sr)MnO$_3$ is also explained., Comment: 7 pages, LaTeX, with 2 PS figures

Exact formulas of diagonal conductivity $\sigma_{xx}$ and Hall conductivity $\sigma_{xy}$ are derived from the Kubo formula in hybridized two-orbital systems with arbitrary band dispersions. On the basis of the theoretical framework for the Fermi liquid based on these formulas, the ground-state properties of the periodic Anderson model with electron correlation and weak impurity scattering are studied on the square lattice. It is shown that imbalance of the mass-renormalization factors in $\sigma_{xx}$ and $\sigma_{xy}$ causes remarkable increase in the valence-fluctuation regime as the f level increases while the cancellation of the renormalization factors causes slight increase in $\sigma_{xx}$ and $\sigma_{xy}$ in the Kondo regime. The Hall coefficient $R_{\rm H}$ shows almost constant behavior in both the regimes. Near half filling, $R_{\rm H}$ is expressed by the total hole density as $R_{\rm H}=1/(\bar{n}_{\rm hole}e)$ while $R_{\rm H}$ approaches zero near quarter filling, which reflects the curvature of the Fermi surface. These results hold as far as the damping rate for f electrons is less than about $10~\%$ of the renormalized hybridization gap. From these results we discuss pressure dependence of residual resistivity and normal Hall effect in Ce- and Yb-based heavy electron systems., Comment: 17 pages, 18 figures

The conductivity of Kubo linear response theory for a quantum well system of many electrons interacting with impurities and confined by a parabolic potential is formulated via a projection operator technique. A line-width function of the optical absorption spectrum is explicitly obtained in the weak coupling approximation up to the second order of the interaction.

An oscillatory behavior of the electrical conductivity tensor component of the quasi-two-dimensional conductors is examined in a lower magnetic field region where an observation of the Shubnikov-de Haas oscillation is not expected. A calculation of the component is carried out with the current vertex corrections in use of Kubo formula, which introduces the transport relaxation time τ t in place of the relaxation time τ s of the energy excitations of the electrons to it. The ratio τ t to τ s is evaluated for a specific model of the quasi-two-dimensional organic conductors.

The dependence of the ionic conductivity on the mobile ion concentration in superionic conductors is studied by making use of the lattice gas model with a hopping term and Kubo's formula. The ionic...

The optical conductivity in high T c Cu oxides is theoretically examined by diagonalizing exactly the Hamiltonian of a Cu 4 O 13 cluster and using the Kubo formula. We show how the optical conductivity caused by the charge transfer from Cu to O ions in the insulator is depressed and how the low-energy conductivity of the Drude type emerges when electron- and hole-carriers are introduced into the CuO 2 plane.

Three decades ago, the quantum Langevin-like equation (Mori formula) was used to reformulate the linear response theory (Kubo formula) in the continued fraction formalism. Since then, the Mori formula has often been used to evaluate transport coefficients, but only within the Born approximation. Very recently, a rigorous closed-form solution to the Mori formula for transport coefficients has been obtained. In the present study, we prove the equivalence of the closed-form solution to the Mori formula and the Kubo formula using the general relations between correlation functions and then comment on the Born approximation.

We extend the derivation of the finite-size Kubo formula for classical systems by Kundu et al. to a finite open quantum system in contact with reservoirs. Starting with the master equation obtained from the quantum repeated interaction model, we examine the linear response, utilizing superoperators defined by virtue of a conservation law. Some generalizations of our method are also discussed.

We have analytically evaluated a quantum correction to the classical Boltzmann conductivity in a single graphene sheet. The effective-mass theory is applied to electronic states and we have collected contributions represented by maximally-crossed diagrams in perturbative expansions of the conductivity by Kubo formula. A logarithmic correction is obtained as is well-known for two-dimensional systems and, surprisingly, it turned out to be both positive and negative dependent only on the interaction-range of scatterers. For the system without symmetry-breaking terms the correction has a negative value due to the quantum interference which enhances the probability of backward scattering, and this phenomenon is called weaklocalization. On the other hand, the spin-orbit interaction which maintains time-reversal symmetry changes the correction into positive since destructive quantum interference is caused by the sign change of spinors by 2π rotation. Simple symmetry considerations lead to the fact that the correction should be negative for a graphene sheet since spin-orbit interaction is weak enough in a graphene sheet, but the situation is not so simple.

Spin-Hall conductivity (SHC) of fully relativistic (4x4 matrix) Dirac electrons is studied based on the Kubo formula aiming at possible application to bismuth and bismuth-antimony alloys. It is found that there are two distinct contributions to SHC, one only from the states near the Fermi energy and the other from all the occupied states. The latter remains even in the insulating state, i.e., when the chemical potential lies in the band-gap, and turns to have the same dependences on the chemical potential as the orbital susceptibility (diamagnetism), a surprising fact. These results are applied to bismuth-antimony alloys and the doping dependence of the SHC is proposed., 4 Pages, 2 figures

Recently, we have developed a theory of Keldysh formalism for mesoscopic systems. The resulting nonequilibrium Kubo formula for differential conductance makes it possible to propose a new formula of the shot noise S h , and thus to study shot noise in correlated systems at any temperature and any bias voltage. Employing this new approach, we analyze shot noise in the Kondo regime through a quantum dot in a symmetric case at zero temperature. Using the renormalized perturbation theory, we prove that, in the leading order of bias voltage, S h is equal to the noise power at zero temperature conventionally used as shot noise. With S h , we calculate the Fano factor for the backscattering current I b : F b = S h /2 e I b . It is shown that the Fano factor takes the universal form of F b =1+4( R -1) 2 /[1+5( R -1) 2 ] determined by the Wilson ratio R for an arbitrary strength of the Coulomb interaction. Using the Wilson ratio R =2, our result coincides with the fractional value of F b =5/3 derived in the Kondo ...

We derive the thermal conductivities of one-dimensional harmonic and anharmonic lattices with self-consistent heat baths (BRV lattice) from the Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we obtain the same result as previous works. However, our approach is heuristic and reveals phonon picture explicitly within the heat transport process. The results for harmonic and anharmonic lattices are compared with numerical calculations from Green-Kubo formula. The consistency between derivation and simulation strongly supports that effective (renormalized) phonons are energy carriers in anharmonic lattices although there exist some other excitations such as solitons and breathers., Comment: 4 pages, 3 figures. accepted for publication in JPSJ

We present a calculation of Seebeck coefficient derived by Kubo–Greenwood formula with the density functional theory. The electronic structure calculation being the Korringa–Kohn–Rsestoker Green's function method with coherent potential approximation and local density functional method (KKR-CPA-LDA). We show the results for transition metals and metal alloys. In particular, the result for palladium-silver alloy shows good agreement with the experimental data. This calculation shows that the role of mean free time associated to each orbital is quite important to obtain an accurate result of the Seebeck coefficient.

We consider the quantum Hall effect of two-dimensional electrons with a periodic potential and study the time dependence of the Hall and longitudinal currents when the electric field is applied abruptly. We find that the currents oscillate in time with very large frequencies because of quantum fluctuation and the oscillations eventually vanish, for their amplitudes decay as 1/t., 16 pages and 8 figures

We study the magneto-optical Kerr effect using fully relativistic calculations. Spin–orbit coupling is dealt with exactly solving the Dirac equation directly and the matrix elements of the Dirac matrices α are used in a fully relativistic expression of the Kubo formula for the optical conductivity derived with a relativistic sum rule. We also perform approximate calculations of the optical conductivity to examine the accuracy of a partly relativistic expression in which the matrix elements of the momentum operator p are used instead. As an example, we carry out calculations for bcc Fe and fcc Ni using the fully relativistic full-potential linear-combination-of-atomic-orbitals method. It is found that the partly relativistic treatment is good for the diagonal optical conductivity while it is not very good for the off-diagonal optical conductivity, the Kerr rotation angle, and the Kerr ellipticity. The results of the present study are compared to those of experimental and other theoretical studies.

The performance of the equilibrium and direct nonequilibrium simulation methods for the calculation of thermal diffusion are examined. Both methods show size dependency for particle number less than 500. The equilibrium simulation should perform for at least 48 ns to obtain statistical errors less than 5%. For a same particle number and simulation length the direct nonequilibrium simulation is one order of magnitude more accurate than the equilibrium one.

The conductance of one-dimensional interacting electron systems is calculated in a manner similar to Landauer's argument for non-interacting systems. Unlike in previous studies in which the Kubo formula was used, the conductance is directly evaluated as the ratio of current $J$ to the chemical potential difference $\Delta \mu$ between right-going and left-going particles. It is shown that both $J$ and $\Delta \mu$ are renormalized by electron-electron (e-e) interactions, but their ratio, the conductance, is not renormalized at all if the e-e interactions are the only scattering mechanism. It is also shown that nonequilibrium current fluctuation at low frequency is absent in such a case. These conclusions are drawn for both Fermi liquids (in which quasi-particles are accompanied with the backflow) and Tomonaga-Luttinger liquids., Comment: 4 pages, No figures

Magnetophonon resonance observed at high electric and magnetic fields in thin n + nn + GaAs structure is shown to be well explained in terms of electric field induced inelastic inter-Landau-level scattering (IILLS). Splitting and inversion of the resonance peaks observed at high electric fields are explained by theoretical analysis of magnetoconductivity σ x x based on Kubo formula. The general oscillatory structure of the magnetoconductivity is given by

Diffusion coefficient of heavy particles in metals is calculated based on Kubo formula, by taking into account the interaction with conduction electrons. By a careful treatment of the thermodynamic limit we obtain the same expression for the coefficient as that derived by Kagan-Klinger method. Through the derivation we can see that though interaction between heavy particles and conduction electrons seems to be enhanced by a vertex renormalization, this enhancement is canceled by the wave-function renormalization. Thus, only the velocity of heavy particles is renormalized by a screening effect.

The concept proposed by Kirkwood that a macroscopic quantity is the time average of the ensemble average of the corresponding dynamical operator is examined in detail. This concept provides us with a new possibility of studying nonequilibrium macroscopic systems. The method to be used here is based on the fact that a time-smoothed density matrix also satisfies the original Liouville-von Neumann equation for the unsmoothed one. Forms of nonequilibritum density matrix are given as exact solutions to it. In characterizing thermodynamically the density operators the use of the Gibbs-Duhem relation is made. A generalized version of Kubo formula is obtained for nonequilibrium systems in the hydrodynamical stage. The present method is also applicable to nonlinear dynamical systems.

The effect of impurities on the phase mode of CDW in a one-dimensional system is studied by taking account of the non-linearity of the problem. Most of the work is based on numerical simulations which are performed using a classical mechanical equation of motion for the phase mode. The existence of critical field for the pinning and depinning is discussed for weak and strong pinning cases. The ohmic frequency-dependent conductivity is calculated by the Kubo formula. The dc conduction in non-ohmic regime is found to be of activation type, the activation energies decreasing with increase of the applied field.

With a view to studying the properties of the optical-absorption edge in a–Si, we calculate in the CPA the density of states (DOS), the absorption spectra and the spectral density on the basis of the site-disordered Abe-Toyozawa model. As the probability distribution for site disorder, we use the bilateral exponential distribution and the distribution defined by an exponential factor with the fourth-order power in its argument as well as the common Gaussian distribution. Our assertion is that, to make the model realistic, we must choose the degree of disorder small enough relative to the band width such that we can identify the three regions of absorption with high, intermediate and low energies. The intermediate region in this case universally shows an exponential behaviour, irrespective of the type of the probability distribution of “static” disorder. We compare the absorption spectra I ( E ) calculated from the Kubo formula with the convolution I conv ( E ) in which the k -selection rule is completely ...

Inadequacy of perturbation treatment in chaotic dynamics is pointed out, especially for phase space distribution function. The coarse graining is introduced into phase space distribution function for describing macroscopic thermodynamic process as a necessary and inevitable procedure for the transition from microscopic to macroscopic levels. A concept of convergence in law is employed for coarse graining. Thus a new approach to the linear response theory is presented, which can remove the various difficulties in the conventional linear response theory. The derivation of the distribution function in the sense of convergence in law is left open, but it is expected that the principal results such as fluctuation-dissipation theorem, Kubo formula for kinetic coefficient remain valid, provided that an appropriate interpretation is applied. Furthermore the entropy is shown to increase and the susceptibility derived in this theory is adiabatic susceptibility expected as a thermodynamic process. The present formul...

The mobility of an ionic defect, H 3 O + defect, in ice is studied on a new model which introduces both coherence in successive transfer-steps of a H 3 O + defect and randomness in transfer direction. States containing a H 3 O + defect are assumed to be coupled with each other by tunneling of proton to form wave-like states as in the case of spin waves in ferromagnetic crystals. The density of states of the coupled system, approximated by a Bethe lattice, is calculated. The mobility of H 3 O + defect is calculated using the Kubo formula. The mobility converges because of the randomness in transfer direction though no other scattering mechanisms are assumed. The value of mobility is obtained as 1.8×10 -5 cm 2 /V·sec at -10°C. Because of coherence the mobility of H 3 O + defect is estimated at about 15 times the mobility calculated for incoherent transfer.

A general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.